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NON ZERO-SUMNESS

  • Zero-sum game
  • Situation where total gains match total losses

    called a strictly competitive game, while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax

    Zero-sum game

    Zero-sum_game

  • Non Zero Sumness
  • 2002 studio album by Planet Funk

    Non Zero Sumness is the debut album released by Italian dance music group Planet Funk. First released on 3 March 2002 in the band's home country by Bustin'

    Non Zero Sumness

    Non_Zero_Sumness

  • Non-zero
  • Topics referred to by the same term

    optical fiber Non zero one, artist collective from London, England Non-zero-sum game, used in game theory and economic theory Non Zero Sumness, 2002 album

    Non-zero

    Non-zero

  • Zero sum (disambiguation)
  • Topics referred to by the same term

    Carol Oates Empty sum Non Zero Sumness Zerosumfree monoid This disambiguation page lists articles associated with the title Zero sum. If an internal link

    Zero sum (disambiguation)

    Zero_sum_(disambiguation)

  • Nonzero: The Logic of Human Destiny
  • Book by Robert Wright

    directed first and foremost by "non-zero-sumness" i.e., the prospect of creating new interactions that are not zero-sum. The principal argument of Nonzero

    Nonzero: The Logic of Human Destiny

    Nonzero:_The_Logic_of_Human_Destiny

  • Planet Funk
  • Italian electronic band

    Italiancharts.com Peaks in Australia: All except noted: Australian peaks Non Zero Sumness and "The Switch": Ryan, Gavin (2011). Australia's Music Charts 1988–2010

    Planet Funk

    Planet Funk

    Planet_Funk

  • Chase the Sun (song)
  • 2000 single by Planet Funk

    and 2001 as the lead single from Planet Funk's debut studio album, Non Zero Sumness (2002). "Chase the Sun" peaked at number five in the United Kingdom

    Chase the Sun (song)

    Chase_the_Sun_(song)

  • Zero-sum thinking
  • Cognitive bias

    Zero-sum thinking perceives situations as zero-sum games, where one person's gain would be another's loss. The term is derived from game theory. However

    Zero-sum thinking

    Zero-sum_thinking

  • Alex Neri
  • Musical artist

    (with Marco Baroni) 2015: Desert Rose (with Federico Grazzini) 2002: Non Zero Sumness 2005: The Illogical Consequence 2006: Static 2009: Planet Funk 2011:

    Alex Neri

    Alex Neri

    Alex_Neri

  • Conflict continuum
  • Concept in social science

    a winner and a loser (a zero-sum game) in a conflict, but was extended to cooperation (a win-win situation and a non-zero sum game), and lets users specify

    Conflict continuum

    Conflict_continuum

  • Zero-sum problem
  • Mathematical problem

    In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite

    Zero-sum problem

    Zero-sum_problem

  • 3SUM
  • Problem in computational complexity theory

    n} real numbers contains three elements that sum to zero. A generalized version, k {\displaystyle k} -SUM, asks the same question on k {\displaystyle k}

    3SUM

    3SUM

  • Alessandro Sommella
  • Italian musician

    formed the band Planet Funk with whom he won a gold disc for the album Non Zero Sumness. Since 2005 he has worked as a music producer with the poet Marcella

    Alessandro Sommella

    Alessandro_Sommella

  • Minimax
  • Decision rule used for minimizing the possible loss for a worst-case scenario

    term commonly used for non-zero-sum games to describe the strategy which maximizes one's own minimum payoff. In non-zero-sum games, this is not generally

    Minimax

    Minimax

  • Dollar auction
  • Game illustrating paradox in rational choice theory

    The dollar auction is a non-zero sum sequential game explored by economist Martin Shubik to illustrate how a short-sighted approach to rational choice

    Dollar auction

    Dollar_auction

  • Absolute gain (international relations)
  • Concept in international relations theory

    effects of an action as well. The theory is also interrelated with a non-zero-sum game which proposes that through use of comparative advantage, all states

    Absolute gain (international relations)

    Absolute_gain_(international_relations)

  • Planet Funk (album)
  • 2009 greatest hits album by Planet Funk

    Canu, M. Baroni and S. Della Monica "Inside All the People" – 4:57 (Non Zero Sumness, 2002) vocals by Dan Black written by Alessandro Neri, Dan Black, Domenico

    Planet Funk (album)

    Planet_Funk_(album)

  • Switch (disambiguation)
  • Topics referred to by the same term

    from Angels with Dirty Faces, 2002 "The Switch", by Planet Funk from Non Zero Sumness, 2002 Switch (American TV series), a 1970s series starring Robert Wagner

    Switch (disambiguation)

    Switch_(disambiguation)

  • Doxing
  • Publication of private details

    2003. The attack is rooted in game theory and was originally dubbed "non-zero-sum games and survivable malware". The attack is summarized in the book Malicious

    Doxing

    Doxing

    Doxing

  • Rogerian argument
  • Conflict-solving technique

    is all the research on the non-zero-sum game, and the need to keep the players on both sides from treating a non-zero-sum game, in which the adversaries

    Rogerian argument

    Rogerian argument

    Rogerian_argument

  • Ransomware
  • Malicious software used in ransom demands

    virus". The attack is rooted in game theory and was originally dubbed "non-zero sum games and survivable malware". The attack can yield monetary gain in

    Ransomware

    Ransomware

  • Sign (mathematics)
  • Number property of being positive or negative

    greater than zero. A number is negative if it is less than zero. A number is non-negative if it is greater than or equal to zero. A number is non-positive

    Sign (mathematics)

    Sign (mathematics)

    Sign_(mathematics)

  • Non-cooperative game theory
  • Type of game involving individual competition

    football game and girl prefers opera). This example is a two-person non-cooperative non-zero sum (TNNC) game with opposite payoffs or conflicting preferences

    Non-cooperative game theory

    Non-cooperative_game_theory

  • Zeros and poles
  • Concept in complex analysis

    type of non-removable singularity of such a function (see essential singularity). Technically, a point z0 is a pole of a function f if it is a zero of the

    Zeros and poles

    Zeros and poles

    Zeros_and_poles

  • Sum of radicals
  • Linear combination of nth roots

    does not solve the problem, because it does not determine the sign of a non-zero sum of radicals. Nested radical, radical expression (one containing a square

    Sum of radicals

    Sum_of_radicals

  • Theory of Games and Economic Behavior
  • Book by John von Neumann and Oskar Morgenstern

    Composition and Decomposition of Games, one on Simple Games and one on General Non-Zero-Sum Games are provided. The final chapter is on Extensions of the Concepts

    Theory of Games and Economic Behavior

    Theory_of_Games_and_Economic_Behavior

  • Traveler's dilemma
  • Non-zero-sum game thought experiment

    game theory, the traveler's dilemma (sometimes abbreviated TD) is a non-zero-sum game in which each player proposes a payoff. The lower of the two proposals

    Traveler's dilemma

    Traveler's_dilemma

  • Zero to the power of zero
  • Mathematical expression with disputed status

    Zero to the power of zero, denoted as 00, is a mathematical expression with different interpretations depending on the context. In certain areas of mathematics

    Zero to the power of zero

    Zero_to_the_power_of_zero

  • Empty sum
  • Summation where the number of terms is zero

    empty sum, or nullary sum, is a summation where the number of terms is zero. The natural way to extend non-empty sums is to let the empty sum be the

    Empty sum

    Empty_sum

  • Superordinate goals
  • factions under realistic group conflict theory, it is necessary to have non-zero sum goals that create a positive interdependence within groups rather than

    Superordinate goals

    Superordinate_goals

  • Paranoid algorithm
  • Algorithm in game theory

    minimize the focal player’s payoff, transforming an n-player non-zero-sum game into a zero-sum game between the focal player and the coalition. The paranoid

    Paranoid algorithm

    Paranoid_algorithm

  • Lump of labour fallacy
  • Misconception in economics about allocation of work

    fallacy of labour scarcity, fixed pie fallacy, and the zero-sum fallacy—due to its ties to zero-sum games. The term "fixed pie fallacy" is also used more

    Lump of labour fallacy

    Lump_of_labour_fallacy

  • Hedonic treadmill
  • Psychological concept

    affecting one's subjective well-being. Headey also found that adopting "non-zero sum" goals, those which enrich one's relationships with others and with society

    Hedonic treadmill

    Hedonic treadmill

    Hedonic_treadmill

  • Nash equilibrium computation
  • Economical computational problem

    computation in two-player zero-sum games is known as min-max optimization. The present page studies the more general problem of non-zero-sum games with many players

    Nash equilibrium computation

    Nash_equilibrium_computation

  • Game theory
  • Mathematical models of strategic interactions

    equilibrium) for non-cooperative games that were not necessarily zero-sum contests. In his 1950 paper, Nash also proved that every finite non-cooperative game

    Game theory

    Game_theory

  • Riemann zeta function
  • Analytic function in mathematics

    on the right is non-zero because Γ(1 − s) has a simple pole, which cancels the simple zero of the sine factor. When s is 0, the zero of the sine factor

    Riemann zeta function

    Riemann zeta function

    Riemann_zeta_function

  • List of games in game theory
  • information. Potentially zero-sum, provided that the prize is split among all players who make an optimal guess. Otherwise non-zero sum. The real value of the

    List of games in game theory

    List_of_games_in_game_theory

  • Stochastic game
  • Concept in game theory

    the value of a two-person zero-sum Γ ∞ {\displaystyle \Gamma _{\infty }} and in defining equilibrium payoffs of a non-zero-sum Γ ∞ {\displaystyle \Gamma

    Stochastic game

    Stochastic_game

  • Sums of three cubes
  • Problem in number theory

    unknown whether the sums of non-negative cubes form a set with non-zero natural density. A nontrivial representation of 0 as a sum of three cubes would

    Sums of three cubes

    Sums of three cubes

    Sums_of_three_cubes

  • Under the Radar Over the Top
  • 2009 studio album by Scooter

    samples Planet Funk's 2001 single "Chase the Sun", from the 2002 album Non Zero Sumness as well as the 2009 songs "Lullaby" by Activator and uses a sample

    Under the Radar Over the Top

    Under_the_Radar_Over_the_Top

  • Common preference
  • Topics referred to by the same term

    preference is an everyone wins situation in a number of places: Zero-sum game#Non-zero-sum Taking Children Seriously Win-win situation This disambiguation

    Common preference

    Common_preference

  • Kaldor–Hicks efficiency
  • State leading to a Pareto-efficient outcome, concerning the compensation principle

    losers. The Kaldor–Hicks criterion is widely applied in game theory's non-zero sum games, such as DOTMLPF, welfare economics, and managerial economics.

    Kaldor–Hicks efficiency

    Kaldor–Hicks efficiency

    Kaldor–Hicks_efficiency

  • 0
  • Whole number

    rendering support, you may see question marks, boxes, or other symbols. 0 (zero, /ˈziː.roʊ/) is a number representing an empty quantity. Adding (or subtracting)

    0

    0

  • Riemann hypothesis
  • Conjecture on zeros of the zeta function

    Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics

    Riemann hypothesis

    Riemann hypothesis

    Riemann_hypothesis

  • Missing market
  • Hypothetical microeconomics situation

    can also be missing if there is a failure of trust or information. In non zero-sum interactions, it is possible that the Nash Equilibrium for individuals

    Missing market

    Missing_market

  • Neofeminism
  • Feminist theory

    femininity in popular culture, rejects zero-sum perceptions of gender relations in favor of a positive-sum (or non-zero-sum) framework. This viewpoint suggests

    Neofeminism

    Neofeminism

  • Indecomposable module
  • algebra, a module is indecomposable if it is non-zero and cannot be written as a direct sum of two non-zero submodules. Indecomposable is a weaker notion

    Indecomposable module

    Indecomposable_module

  • Competition
  • Rivalry for a goal which cannot be shared

    shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, individuals

    Competition

    Competition

    Competition

  • Eilon Solan
  • Israeli mathematician

    Behavior, 47, 172–199. - Shmaya, E. and Solan, E. (2004). Two Player Non Zero-Sum Stopping Games in Discrete Time. The Annals of Probability, 32, 2733–2764

    Eilon Solan

    Eilon Solan

    Eilon_Solan

  • Witt group
  • Algebra term

    w\rangle \!\rangle =\langle 1,-w\rangle } with w {\displaystyle w} a non-zero sum of squares. If k is not formally real, then the Witt group is torsion

    Witt group

    Witt_group

  • Nash equilibrium
  • Solution concept of a non-cooperative game

    hypergraphs. For zero-sum games this was shown by J. Edmonds and D. R. Fulkerson. Later this result was extended for the non-zero sum case. Interestingly

    Nash equilibrium

    Nash_equilibrium

  • Negotiation
  • Dialogue intended to reach an agreement

    integrative negotiation, a different concept (as outlined above) related to a non-zero-sum approach to creating value in negotiations. Integrated negotiation was

    Negotiation

    Negotiation

    Negotiation

  • Zero-inflated model
  • Statistical model allowing for frequent zero values

    a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent zero-valued

    Zero-inflated model

    Zero-inflated_model

  • Collective action problem
  • Type of social dilemma

    Ostrom Game theory Identity politics Moral economy Nash equilibrium Non-zero-sum Prisoner's dilemma Rationality Social trap Strategic games Superimposed

    Collective action problem

    Collective_action_problem

  • Maximum subarray problem
  • Problem in computer science

    convention, the sum of all values of the empty subarray is zero.) Each number in the input array A could be positive, negative, or zero. For example, for

    Maximum subarray problem

    Maximum subarray problem

    Maximum_subarray_problem

  • Core (game theory)
  • Set in game theory

    Morgenstern considered it an interesting concept, they only worked with zero-sum games where the core is always empty. The modern definition of the core

    Core (game theory)

    Core_(game_theory)

  • Association football tactics
  • Notable football skills and tactics

    "Modeling Tactical Changes of Formation in Association Football as a Non-Zero-Sum Game". Journal of Quantitative Analysis in Sports. 5 (3): 1–15. doi:10

    Association football tactics

    Association football tactics

    Association_football_tactics

  • Information economics
  • Branch of microeconomics

    • Françoise Forges, 1992. "Repeated Games of Incomplete Information: Non-Zero-Sum," Handbook of Game Theory with Economic Applications, v. 1, Elsevier

    Information economics

    Information_economics

  • Intransitive game
  • Zero-sum game where competitions between strategies contain a cycle

    An intransitive or non-transitive game is a zero-sum game in which pairwise competitions between the strategies contain a cycle. If strategy A beats strategy

    Intransitive game

    Intransitive_game

  • Social trading
  • Form of investing

    each other but rather – against the market, this situation becomes a non zero-sum game, hence incentivizing the users to share as much information as possible

    Social trading

    Social_trading

  • Lean higher education
  • management is responsive to the needs of multiple stakeholders in a non-zero-sum fashion and is therefore well-suited for the governance and ongoing improvement

    Lean higher education

    Lean_higher_education

  • Gauss–Newton algorithm
  • Mathematical algorithm

    Newton's method to iteratively approximate zeroes of the components of the sum, and thus minimizing the sum. In this sense, the algorithm is also an effective

    Gauss–Newton algorithm

    Gauss–Newton algorithm

    Gauss–Newton_algorithm

  • Aldo Rustichini
  • Italian-born American economist

    research has established that the probability of cooperation in repeated non-zero-sum games increases with the average intelligence of the group. His works

    Aldo Rustichini

    Aldo Rustichini

    Aldo_Rustichini

  • Minkowski addition
  • Sums vector sets A and B by adding each vector in A to each vector in B

    ball, centered at 0 (the non-zero assumption is needed because the open ball of radius 0 is the empty set). The Minkowski sum of a closed ball and an open

    Minkowski addition

    Minkowski addition

    Minkowski_addition

  • 50 (number)
  • Natural number

    following 49 and preceding 51. Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways. 50 is an unsigned Stirling number

    50 (number)

    50_(number)

  • Military simulation
  • Type of simulation

    techniques is known as game theory—a commonly used method is that of non-zero-sum analysis, in which score tables are drawn up to enable selection of a

    Military simulation

    Military simulation

    Military_simulation

  • F-Zero
  • Video game series

    F-Zero is a series of racing games published by Nintendo, developed by Nintendo EAD and other third-party companies. The original F-Zero was released for

    F-Zero

    F-Zero

  • Pole–zero plot
  • Diagram showing the singularities of a given control system's transfer function

    convergence (ROC) Minimum phase / non minimum phase A pole-zero plot shows the location in the complex plane of the poles and zeros of the transfer function of

    Pole–zero plot

    Pole–zero plot

    Pole–zero_plot

  • Infinite product
  • Mathematical concept

    to 0 if there are only a finite number of zero factors and the product of the non-zero factors is non-zero, but for simplicity we will not allow that

    Infinite product

    Infinite_product

  • Zero degrees of freedom
  • In statistics, the non-central chi-squared distribution with zero degrees of freedom can be used in testing the null hypothesis that a sample is from a

    Zero degrees of freedom

    Zero_degrees_of_freedom

  • Riemann integral
  • Basic integral in elementary calculus

    _{a}^{b}f(x)\,dx.} On non-compact intervals such as the real line, this is false. For example, take fn(x) to be n−1 on [0, n] and zero elsewhere. For all

    Riemann integral

    Riemann integral

    Riemann_integral

  • Trailing zero
  • Zero after the final non-zero digit of a number

    trailing zeros in a non-zero base-b integer n equals the exponent of the highest power of b that divides n. For example, 14000 has three trailing zeros and

    Trailing zero

    Trailing_zero

  • List of types of numbers
  • \mathbb {Q} } ): Numbers that can be expressed as a ratio of an integer to a non-zero integer. All integers are rational, but there are rational numbers that

    List of types of numbers

    List_of_types_of_numbers

  • Direct sum
  • Algebraic structure formed from a collection of algebraic structures

    the direct sum usually maintains that structure (as an example of the opposite, the direct sum of fields is not a field as it contains zero divisors).

    Direct sum

    Direct_sum

  • Zero-point energy
  • Lowest possible energy of a quantum system or field

    Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly

    Zero-point energy

    Zero-point energy

    Zero-point_energy

  • Bianchi classification
  • Lie algebra classification

    semidirect products of R2 by R, where the matrix M has non-zero distinct real eigenvalues with non-zero sum. The algebras are solvable and not unimodular. The

    Bianchi classification

    Bianchi_classification

  • Frank George Woollard
  • British mechanical engineer

    understood that to achieve flow production, management practice had to be non-zero-sum, meaning that workers had to be respected and also benefit from flow

    Frank George Woollard

    Frank_George_Woollard

  • Gauss sum
  • Sum in algebraic number theory

    Consequently, G(χ) is non-zero precisely when ⁠N/N0⁠ is squarefree and relatively prime to N0. Other relations between G(χ) and Gauss sums of other characters

    Gauss sum

    Gauss_sum

  • Degree of a polynomial
  • Mathematical concept

    terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer

    Degree of a polynomial

    Degree_of_a_polynomial

  • Supernode (circuit)
  • Theoretical construct in circuit theory

    required between two non-reference nodes. It is related to Kirchhoff's current law which states that the total or algebraic sum of currents meeting at

    Supernode (circuit)

    Supernode (circuit)

    Supernode_(circuit)

  • Explicit formulae for L-functions
  • Mathematical concept

    formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by Riemann (1859)

    Explicit formulae for L-functions

    Explicit_formulae_for_L-functions

  • Thermodynamic temperature
  • Measure of temperature relative to absolute zero

    is a physical quantity that measures temperature starting from absolute zero, the point at which particles have minimal thermal motion. Thermodynamic

    Thermodynamic temperature

    Thermodynamic temperature

    Thermodynamic_temperature

  • Summation
  • Addition of several numbers or other values

    no summands, then the evaluated sum is zero, because zero is the identity for addition. This is known as the empty sum. These degenerate cases are usually

    Summation

    Summation

  • Semisimple Lie algebra
  • Direct sum of simple Lie algebras

    semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any non-zero proper ideals.) Throughout

    Semisimple Lie algebra

    Semisimple Lie algebra

    Semisimple_Lie_algebra

  • Simple module
  • Type of module over a ring

    are non-zero and have no non-zero proper submodules. Equivalently, a module M is simple if and only if every cyclic submodule generated by a non-zero element

    Simple module

    Simple_module

  • Hamming weight
  • Number of nonzero symbols in a string

    that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length

    Hamming weight

    Hamming weight

    Hamming_weight

  • Divergent series
  • Infinite series that is not convergent

    the partial sums of the series does not have a finite limit. If a series converges, the individual terms of the series must approach zero. Thus any series

    Divergent series

    Divergent_series

  • Brier score
  • Measure of the accuracy of probabilistic predictions

    between zero and one, since this is the square of the largest possible difference between a predicted probability (which must be between zero and one)

    Brier score

    Brier_score

  • Norm (mathematics)
  • Length in a vector space

    metric from zero is not homogeneous in the non-zero point; indeed, the distance from zero remains one as its non-zero argument approaches zero. However,

    Norm (mathematics)

    Norm_(mathematics)

  • Evil number
  • Class of binary number

    evil number is a non-negative integer that has an even number of 1s in its binary expansion. These numbers give the positions of the zero values in the Thue–Morse

    Evil number

    Evil_number

  • Undefined (mathematics)
  • Expression which is not assigned an interpretation

    by zero. This operation is undefined in arithmetic, and therefore deductions based on division by zero can be contradictory. If we assume that a non-zero

    Undefined (mathematics)

    Undefined_(mathematics)

  • Mathematical economics
  • Branch of applied mathematics

    Retrieved 2020-05-28. Gillies, D. B. (1969). "Solutions to general non-zero-sum games". In Tucker, A. W.; Luce, R. D. (eds.). Contributions to the Theory

    Mathematical economics

    Mathematical_economics

  • Empty set
  • Mathematical set containing no elements

    the sum of the elements of the empty set (the empty sum) is zero. The reason for this is that zero is the identity element for addition. Similarly, the

    Empty set

    Empty set

    Empty_set

  • Symmetrical components
  • Method of analysis of unbalanced three-phase power systems

    known as zero sequence or homopolar) is one-third the sum of the original three phasors. Sequence 1 (positive sequence) is one-third the sum of the original

    Symmetrical components

    Symmetrical components

    Symmetrical_components

  • Collective self-limitation
  • Expression of collective autonomy

    ISBN 3-518-11365-8. OCLC 16165613. Swingle, Paul G. (1970). "Exploitative behavior in non-zero-sum games". Journal of Personality and Social Psychology. 16 (1): 121–132

    Collective self-limitation

    Collective_self-limitation

  • Jean-François Mertens
  • Belgian game theorist (1946–2012)

    in 1981 by Jean-François Mertens and Abraham Neyman. The study of the non-zero-sum with a general state and action spaces attracted much attention, and

    Jean-François Mertens

    Jean-François Mertens

    Jean-François_Mertens

  • Divya Narendra
  • American businessman (born 1982)

    18, 1982) is an American businessman. He is the CEO and co-founder of SumZero along with Harvard classmate Aalap Mahadevia. He also co-founded HarvardConnection

    Divya Narendra

    Divya Narendra

    Divya_Narendra

  • Zero of a function
  • Point where function's value is zero

    polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that

    Zero of a function

    Zero of a function

    Zero_of_a_function

  • Sum of two cubes
  • Mathematical polynomial formula

    in the case of exponent 3 states that the sum of two non-zero integer cubes does not result in a non-zero integer cube. The first recorded proof of the

    Sum of two cubes

    Sum of two cubes

    Sum_of_two_cubes

  • Von Mangoldt function
  • Function on an integer n which is log(p) if n equals p^k and zero otherwise

    explicit formula for ψ ( x ) {\displaystyle \psi (x)} involving a sum over the non-trivial zeros of the Riemann zeta function. This was an important part of

    Von Mangoldt function

    Von_Mangoldt_function

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