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Modular unit in mathematics
In mathematics, elliptic units are certain units of abelian extensions of imaginary quadratic fields constructed using singular values of modular functions
Elliptic_unit
Mathematical function
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as
Jacobi_elliptic_functions
Concept in mathematics
cusps (images of infinity). Cyclotomic unit Elliptic unit Kubert, Daniel S.; Lang, Serge (1981), Modular units, Grundlehren der Mathematischen Wissenschaften
Modular_unit
Special function defined by an integral
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied
Elliptic_integral
Algebraic curve in mathematics
mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined
Elliptic_curve
Cone with an elliptical base
An elliptical cone is a cone with an elliptical base. It is a generalization of the circular cone and a special case of the generalized cone. The term
Elliptic_cone
Non-Euclidean geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel
Elliptic_geometry
Cohomology theory related to elliptic curves
In mathematics, elliptic cohomology is a cohomology theory related to elliptic curves and modular forms. Call a cohomology theory A∗ even periodic when
Elliptic_cohomology
Class of periodic mathematical functions
analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because
Elliptic_function
Algebraic number field unit
basis Bn of the cyclotomic units can be constructed with the property that Bd ⊆ Bn for d | n. Elliptic unit Modular unit Washington, Theorem 8.2 Washington
Cyclotomic_unit
Class of mathematical functions
In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This
Weierstrass_elliptic_function
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
Mathematical concept
introduced by Kolyvagin (1990) in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper Kolyvagin (1988) and the
Euler_system
Gives the rank of the group of units in the ring of algebraic integers of a number field
conjecture states that this determinant is non-zero. Elliptic unit Cyclotomic unit Shintani's unit theorem Elstrodt 2007, §8.D Stevenhagen, P. (2012).
Dirichlet's_unit_theorem
Stationary exercise machine
When the unit was complete, Feeder offered the customer a test drive. The sale was closed and the start of the Elliptical began. The unit name was changed
Elliptical_trainer
Signal processing filter
An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a signal processing filter
Elliptic_filter
Rational function of the form (az + b)/(cz + d)
modular group; it is central to the theory of many fractals, modular forms, elliptic curves and Pellian equations. Möbius transformations can be more generally
Möbius_transformation
Quadric surface with one axis of symmetry and no center of symmetry
paraboloid is hyperbolic if the factors are real; elliptic if the factors are complex conjugate. An elliptic paraboloid is shaped like an oval cup and has
Paraboloid
Geometric figure
In geometry, the unit hyperbola is the set of points ( x , y ) {\displaystyle (x,y)} in the Cartesian plane that satisfy the implicit equation x 2 − y
Unit_hyperbola
Polarization of electromagnetic radiation
In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an
Elliptical_polarization
In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map
Dixon_elliptic_functions
Quaternion of norm 1 (unit quaternion)
illustrate elliptic geometry, in particular elliptic space, a three-dimensional realm of rotations. The versors are the points of this elliptic space, though
Versor
In mathematics, the conductor of an elliptic curve over the field of rational numbers (or more generally a local or global field) is an integral ideal
Conductor of an elliptic curve
Conductor_of_an_elliptic_curve
Topic in algebraic number theory
principle to some form of the S-unit equation: a notable example is Siegel's theorem on integral points on elliptic curves, and more generally superelliptic
S-unit
American mathematician at Duke University
classical and p-adic L-functions". Darmon, Henri; Dasgupta, Samit (2006). "Elliptic units for real quadratic fields". Annals of Mathematics. 163 (1): 301–346
Samit_Dasgupta
Mean distance between Earth and the Sun
The astronomical unit (symbol: au or AU) is a unit of length defined as 149597870700 m. Historically, the astronomical unit was conceived as the average
Astronomical_unit
Specifies the orbit of an object in space
In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed
Mean_anomaly
Plane curve
quadrics: Ellipsoid Elliptic cone Elliptic cylinder Hyperboloid of one sheet Hyperboloid of two sheets Ellipsoid Elliptic cone Elliptic cylinder Hyperboloid
Ellipse
Units that are not part of a coherent system
of units of measurement in active use, which do not form part of a coherent system of measurement. Many of the items listed here are colloquial units based
List of non-coherent units of measurement
List_of_non-coherent_units_of_measurement
Topics referred to by the same term
physics Exacoulomb (EC), an SI unit for electric charge equal to 1018 coulomb Early Cycladic, an archaeological period Elliptic curve, in mathematics Emergent
EC
Film by Christopher Nolan
felt the teaser previewed The Odyssey "through suggestion and cleverly elliptical editing". /Film's Rick Stevenson wrote that the teaser continued Nolan's
The_Odyssey_(2026_film)
Unit of time based on Earth's orbit
A year is a unit of time based on how long it takes the Earth to orbit the Sun. In scientific use, the tropical year (approximately 365 solar days, 5 hours
Year
Proposed lower bound on the Mahler measure for polynomials with integer coefficients
in 1996 obtained C ≥ 1/4 for D ≥ 2. Let E / K {\displaystyle E/K} be an elliptic curve defined over a number field K {\displaystyle K} , and let h ^ E :
Lehmer's_conjecture
lemma has been generalized to describe the behavior of the solution to an elliptic problem as it approaches a point on the boundary where its maximum is attained
Hopf_lemma
Group of real 2×2 matrices with unit determinant
that is not open. The eigenvalues for an elliptic element are both complex, and are conjugate values on the unit circle. Such an element is conjugate to
SL2(R)
Analytic function on the upper half-plane with a certain behavior under the modular group
Chandrasekharan, K. (1985). Elliptic functions. Springer-Verlag. p. 15. ISBN 3-540-15295-4. Kubert, Daniel S.; Lang, Serge (1981), Modular units, Grundlehren der
Modular_form
Two geometries based on axioms closely related to those specifying Euclidean geometry
for a family of Riemannian metrics on the unit ball in Euclidean space. The simplest of these is called elliptic geometry and it is considered a non-Euclidean
Non-Euclidean_geometry
Measure of time as per Jain scriptures
Jain units of time range from an infinitesimally small, indivisible measurement of time known as a samayā to innumerable lengths of time measured in sagaropama
Jain_units_of_time
Symmetric holomorphic function
branch points of a ramified double cover of the projective line by the elliptic curve C / ⟨ 1 , τ ⟩ {\displaystyle \mathbb {C} /\langle 1,\tau \rangle
Modular_lambda_function
Special mathematical function
In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions. This function
Nome_(mathematics)
Sphere with radius one, usually centered on the origin of the space
generally, the unit n-sphere is an n-sphere of unit radius in (n+1)-dimensional Euclidean space; the unit circle is a special case, the unit 1-sphere
Unit_sphere
Mathematical result in differential geometry
proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related
Atiyah–Singer_index_theorem
French mathematician (1975–2024)
webpage". Bergeron, Nicolas; Charollois, Pierre; García, Luis (2023). "Elliptic units for complex cubic fields (on Eisenstein's Jugendtraum)". arXiv:2311
Nicolas_Bergeron
Differential operator in mathematics
tasks, such as blob and edge detection. The Laplacian is the simplest elliptic operator and is at the core of Hodge theory as well as the results of de
Laplace_operator
Amount of matter present in an object
object's gravitational attraction to other bodies. The unit of mass in the International System of Units (SI) is the kilogram (kg). Mass can also be understood
Mass
Modular function in mathematics
weight 0. Classically, the j-invariant was studied as a parameterization of elliptic curves over ℂ, but it also has surprising connections to the symmetries
J-invariant
Simply connected Riemann surface is equivalent to an open disk, complex plane, or sphere
Riemann sphere as universal cover ("elliptic"), those with the plane as universal cover ("parabolic") and those with the unit disk as universal cover ("hyperbolic")
Uniformization_theorem
Topics referred to by the same term
Access Protocol Symmetric group or Sn n-sphere or Sn sn (elliptic function), one of Jacobi's elliptic functions Sigma notation, also known as a summation SN
SN
Laws describing planetary orbits
constant, T is the orbital period and a is the elliptical semi-major axis, and AU is the astronomical unit – the average distance from earth to the sun
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
One-dimensional complex manifold
{\displaystyle \tau } is any complex non-real number. These are called elliptic curves. Important examples of non-compact Riemann surfaces are provided
Riemann_surface
Special functions of several complex variables
when arranged in a lattice?" geometry: "what are the shape properties of elliptic curves?" and others, including abelian varieties, moduli spaces, quadratic
Theta_function
Canonical set of three elliptic integrals
forms of elliptic integrals are a canonical set of three elliptic integrals to which all others may be reduced. Legendre chose the name elliptic integrals
Legendre_form
Digital asset using a distributed ledger
Half a Billion Dollars has Been Laundered Through a Cross-chain Bridge". Elliptic Connect. 8 October 2022. Archived from the original on 2 April 2023. Retrieved
Cryptocurrency
Decentralized digital cryptocurrency
smart contracts and Lightning Network. Before, bitcoin only used a custom elliptic curve with the ECDSA algorithm to produce signatures. In September 2021
Bitcoin
prefigured by earlier results of Charles Morrey from 1938 on quasi-linear elliptic partial differential equations. The theorem of Ahlfors and Bers states
Measurable Riemann mapping theorem
Measurable_Riemann_mapping_theorem
Study of health and disease within a population
Filipinos did not voluntarily seek vaccination. In 1902 Batangas, military units accompanied by physicians would enter houses and vaccinate inhabitants.
Epidemiology
Fundamental trigonometric functions
Discrete sine transform Dixon elliptic functions Euler's formula Generalized trigonometry Hyperbolic function Lemniscate elliptic functions Law of sines List
Sine_and_cosine
1971 studio album by Faces
(one co-written with keyboardist Ian McLagan). Of these, "Debris", an elliptical but emotional examination of father-son relationships, was chosen as the
A Nod Is As Good As a Wink... to a Blind Horse
A_Nod_Is_As_Good_As_a_Wink..._to_a_Blind_Horse
Class of expander graphs arising in computational number theory
number theory and have been applied in elliptic-curve cryptography. Their vertices represent supersingular elliptic curves over finite fields and their edges
Supersingular_isogeny_graph
Hair loss treatment
Follicular unit transplantation (FUT) is a hair restoration technique, also known as the strip procedure, where a patient's hair is transplanted in naturally
Follicular unit transplantation
Follicular_unit_transplantation
10 September 2026. "curve #273". Elliptic Curve Rank Leaderboard. Retrieved 21 September 2026. "curve #302". Elliptic Curve Rank Leaderboard. Retrieved
List of mathematical discoveries made with artificial intelligence
List_of_mathematical_discoveries_made_with_artificial_intelligence
Complex numbers with unit norm and both real and imaginary parts rational numbers
In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x2 + y2 = 1
Group of rational points on the unit circle
Group_of_rational_points_on_the_unit_circle
Third planet from the Sun
phenomenon known as length-of-day variation. Earth's orbit is slightly elliptical rather than perfectly circular, and its closest approach to the Sun is
Earth
Concept in mathematics
In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing
Drinfeld_module
Canadian-American mathematician (1925–2020)
previously understood for second-order elliptic partial differential equations, to the general setting of elliptic systems. With Basilis Gidas and Wei-Ming
Louis_Nirenberg
Distance from center of Earth to center of Moon
uncertainty of a decimeter for the semi-major axis. However, due to its elliptical orbit with varying eccentricity, the instantaneous distance varies with
Lunar_distance
Type of investment fraud
Manet, has been identified as a director of Huione Pay within the group. Elliptic described Huione Guarantee as a Telegram-based marketplace widely used
Pig_butchering_scam
History of Istanbul under Ottoman rule
of the upper classes began to speak French, and European carriages on elliptical springs appeared on the streets. Under Abdulmejid, non-Muslims were again
Istanbul during the Ottoman Empire
Istanbul_during_the_Ottoman_Empire
Commemorative coins of the Eurozone 2010-2019
incisively brings out the tension between the dominant tower and the elliptical structure of the church. The slightly exaggerated flight of steps has
List of 2 euro commemorative coins (2010–2019)
List_of_2_euro_commemorative_coins_(2010–2019)
Function with two complex number "periods"
zero. Elliptic function Abel elliptic functions Jacobi elliptic functions Weierstrass elliptic functions Lemniscate elliptic functions Dixon elliptic functions
Doubly_periodic_function
Dubai-based cryptocurrency exchange
third-party provider. Blockchain analytics firms Arkham Intelligence and Elliptic claimed they were able to trace the hack to Lazarus Group, an advanced
Bybit
Type of differential equation
classical topics, on which there is still much active research, include elliptic and parabolic partial differential equations, fluid mechanics, Boltzmann
Partial_differential_equation
Topics referred to by the same term
field (mathematics), abbreviated from the German Körper K, the complete elliptic integral of the first kind K-distribution, a family of continuous probability
K_(disambiguation)
Hindu units of time are described in Hindu texts ranging from microseconds to trillions of years, including cycles of cosmic time that repeat general
Hindu_units_of_time
Inequality for Harmonic Functions
J. Moser (1961, 1964) generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Such results can be used to
Harnack's_inequality
Mathematical structure
functions, but certainly the unit circle is defined by a polynomial equation. (The same remark applies to elliptic curves and elliptic functions; and in fact
Transcendental_curve
Problem about mathematical number fields
case of any imaginary quadratic field, by using modular functions and elliptic functions chosen with a particular period lattice related to the field
Hilbert's_twelfth_problem
Topics referred to by the same term
Domain Nameserver DOS Navigator, a DOS file manager dn (elliptic function), one of Jacobi's elliptic functions Dn, a Coxeter–Dynkin diagram Dn, a dihedral
DN
Parameter in the gravitational two-body problem
typically expressed in units of MJkg (megajoule per kilogram) or km2s2 (squared kilometer per squared second). For an elliptic orbit the specific orbital
Specific_orbital_energy
Skyscraper in Manhattan, New York
ground level, the building's northern prow is cantilevered from a pair of elliptical girders, while the southwest and southeast corners contain diagonal floor
Flatiron_Building
Israeli mathematician (1922–2025)
decay of eigenfunctions for elliptic operators. In 1965 he published a book on linear boundary value problems for elliptic partial differential equations
Shmuel_Agmon
Star system in the Centaurus constellation
period of 79 years. Their elliptical orbit is eccentric, so that the distance between A and B varies from 35.6 astronomical units (AU), or about the distance
Alpha_Centauri
Unit of information
information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted
Data
Number, approximately 3.14
Chudnovsky algorithm involves in an essential way the j-invariant of an elliptic curve. Modular forms are holomorphic functions in the upper half plane
Pi
System of stars and interstellar matter
Galaxies are categorised according to their visual characteristics such as elliptical, spiral, or irregular. The Milky Way is an example of a spiral galaxy
Galaxy
Complete set of items that share at least one property in common
Structural equation model Factor analysis Multivariate distributions Elliptical distributions Normal Time-series General Decomposition Trend Stationarity
Statistical_population
melius abundare quam deficere Better too much than not enough Also used in elliptical form as melius abundare. meliora better things Carrying the connotation
List_of_Latin_phrases_(full)
British single-seat WWII fighter aircraft
Vickers-Armstrong from 1928. Mitchell modified the Spitfire's distinctive elliptical wing (designed by Beverley Shenstone) with innovative sunken rivets to
Supermarine_Spitfire
Number of "holes" of a surface
{\displaystyle X} (its manifold of complex points). For example, the definition of elliptic curve from algebraic geometry is connected non-singular projective curve
Genus_(mathematics)
Individual entity for statistical purposes
In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a "random variable".
Statistical_unit
Overview of how Japanese verbs conjugate
itte okure → ittokure (行っておくれ→行っとくれ; '[do me a favor and] go!'), or be elliptically omitted as in itte kudasai → itte (行ってください→行って; '[do me a favor and]
Japanese_conjugation
American automobile model (1925–1937)
semi-elliptic springs all round, and after experiments with hydraulic brakes, Auburn opted for mechanical brakes. The three-speed gearbox was in unit with
Auburn_Speedster
Whole number
print typefaces made the capital letter O more rounded than the narrower, elliptical digit 0. Typewriters originally made no distinction in shape between O
0
are circular, the middle and largest stone circle, however, is slightly elliptical. King Doniert's Stone Standing Cross 9th century Remains Consists of two
List of English Heritage properties
List_of_English_Heritage_properties
Russian technology company
aimed at stealing technical information from its research and development unit on how users were authenticated. An investigation by Kaspersky Lab attributed
Yandex
American business jet
displays with three 14-inch (36 cm) screens, and an autothrottle system. The elliptical winglets that were available as an aftermarket option on the Citation
Cessna_Citation_X
Concept in celestial mechanics
angular speed, and T is the orbital period. This can be generalized for elliptic orbits: μ=4π2a3T2, where a is the semi-major axis, which is Kepler's third
Standard gravitational parameter
Standard_gravitational_parameter
Galaxy in the constellation Leo
the intracluster gas. With an ellipticity of 0.32±0.02, the stellar distribution is far from spherical. In solar units, the total stellar luminosity is
Abell_1201_BCG
Locus of the zeros of a polynomial of degree two
are no real points: ε1=ε2=1 (imaginary ellipsoid), ε1=0,ε2=1 (imaginary elliptic cylinder), and ε4=1 (pair of complex conjugate parallel planes, a reducible
Quadric
the list. The Birch and Swinnerton-Dyer conjecture can be formulated for elliptic curves over any number field, and generalizations for more general arithmetic
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
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ELLIPTIC UNIT
ELLIPTIC UNIT
ELLIPTIC UNIT
ELLIPTIC UNIT
ELLIPTIC UNIT
ELLIPTIC UNIT
ELLIPTIC UNIT
ELLIPTIC UNIT
ELLIPTIC UNIT
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