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Concept in number theory
In number theory, the adele ring is a construction that combines all local versions of a global field into one object. For the rational numbers, these
Adele_ring
Semitopological group in abstract algebra
G(\mathbb {A} _{K})} , where A K {\displaystyle \mathbb {A} _{K}} is the adele ring of K {\displaystyle K} . For a linear algebraic group, G ( A K ) {\displaystyle
Adelic_algebraic_group
English singer-songwriter (born 1988)
Adele Laurie Blue Adkins (/əˈdɛl/ ə-DEL; born 5 May 1988) is an English singer and songwriter. Regarded as a British cultural icon, she is known for her
Adele
Concept in number theory
non-archimedean places. Equivalently, it is the group of invertible elements of the adele ring A K {\displaystyle \mathbb {A} _{K}} , equipped with a topology finer
Idele_group
Mathematical concept
{\displaystyle G(\mathbb {A} )/G(k)} , where A {\displaystyle \mathbb {A} } is the adele ring of k. Tamagawa numbers were introduced by Tamagawa (1966), and named after
Tamagawa_number
Algebraic structure with addition and multiplication
of a projective limit of rings (see below). Another application is a restricted product of a family of rings (cf. adele ring). Given a symbol t (called
Ring_(mathematics)
Topics referred to by the same term
Look up Adele or adele in Wiktionary, the free dictionary. Adele (born 1988) is an English singer-songwriter. Adele may also refer to: Adele (given name)
Adele_(disambiguation)
Book about number theory
p-adic completions. In this setting, the adeles (or valuation vectors) give a natural locally compact ring in which all the valuations are brought together
Basic_Number_Theory
Branch of number theory
Considering all the places of the field together produces the adele ring of the number field. The adele ring allows one to simultaneously track all the data available
Algebraic_number_theory
Construction for topological groups
compact group. The best known example of this construction is that of the adele ring and idele group of a global field. Direct sum Fröhlich, A.; Cassels, J
Restricted_product
Mathematical concept
the properties of automorphic representations of reductive groups over adele rings and the unitary representations of reductive groups over local fields
Arthur's_conjectures
Conjectures connecting number theory and geometry
general linear group GL(n) over the adele ring of Q {\displaystyle \mathbb {Q} } (the rational numbers). (This ring tracks all the completions of Q , {\displaystyle
Langlands_program
Complex-valued smooth functions of the upper half plane (harmonic analysis topic)
_{\mathbb {Q} }} be the ring of rational adeles, A fin {\displaystyle \mathbb {A} _{\text{fin}}} the ring of the finite (rational) adeles and for a prime number
Maass_wave_form
Area of mathematical analysis
questions about L-functions are formulated using harmonic analysis on the adele ring and idele group. Harmonic analysis, in this latter sense, is closely connected
Harmonic_analysis
British mathematician and logician
theory of products of algebraic structures. The adele ring was introduced by Claude Chevalley. (The word "adele" is short for "additive idele"[2] and it was
Angus_Macintyre
1970 mathematics text by Jacquet and Landlands
in terms of the representation theory of GL(2) over local fields and adele rings of global fields, and prove the Jacquet–Langlands correspondence. A second
Automorphic_Forms_on_GL(2)
respect to the subspace topology. An example of this situation is the adele ring of a global field; its unit group, called the idele group, is not a topological
Topological_ring
Type of mathematical space
compact set. Any global field K is a discrete additive subgroup of its adele ring, and the quotient space is compact. This was used in John Tate's thesis
Compact_space
theorem Totally real field Local field p-adic number p-adic analysis Adele ring Idele group Idele class group Adelic algebraic group Global field Hasse
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
Type of complex number
denoted by A {\displaystyle \mathbb {A} } , but that usually denotes the adele ring). Every root of a polynomial equation whose coefficients are algebraic
Algebraic_number
French mathematician (1906-1998)
Deligne, who completed the most difficult step in 1973. Weil introduced the adele ring in the late 1930s, following Claude Chevalley's lead with the ideles,
André_Weil
global field k, and A the adele ring of k. If S is a non-empty finite set of places of k, then we write AS for the ring of S-adeles and AS for the product
Approximation in algebraic groups
Approximation_in_algebraic_groups
B C D E F G H I K L M N O P Q R S T U V W X Z See also References A – adele ring or algebraic numbers. a.a.s. – asymptotically almost surely. AC – Axiom
List of mathematical abbreviations
List_of_mathematical_abbreviations
Modular form
group G {\displaystyle G} (over A {\displaystyle \mathbb {A} } , the adele ring), an automorphic form ϕ {\displaystyle \phi } on U ( A ) M ( k ) ∖ G {\displaystyle
Cusp_form
American mathematician (1925–2019)
of automorphic forms and their L-functions, notably by its use of the adele ring, its self-duality and harmonic analysis on it; independently and a little
John_Tate_(mathematician)
British singer (born 1987)
Adele Emily Sandé (/ˈsændeɪ/ SAN-day; previously Gouraguine; born 10 March 1987), known professionally as Emeli Sandé, is a British singer and songwriter
Emeli_Sandé
distinct prime factors of abc raised to the power of 1+ε is less than c. adele Adele ring algebraic number An algebraic number is a number that is the root of
Glossary_of_number_theory
Set with associative invertible operation
include the group of points of an algebraic group over a local field or adele ring; these are basic to number theory Galois groups of infinite algebraic
Group_(mathematics)
Finite extension of the rationals
pertaining to all local fields attached to K {\displaystyle K} , the adele ring is set up. A multiplicative variant is referred to as ideles. Algebraic
Algebraic_number_field
Mathematical theories
Hardy–Littlewood circle method in analytic number theory, and the use of adele rings, making this one of the unifying principles across number theory. Category:Localization
Local_analysis
{\displaystyle k} be a number field, A {\displaystyle \mathbb {A} } be its adele ring, k × {\displaystyle k^{\times }} be the subgroup of invertible elements
Waldspurger_formula
Type of Dirichlet series associated to number field extensions
{\text{GL}}(n,A_{K})} , where A K {\displaystyle \mathbf {A} _{K}} be adele ring for K {\displaystyle K} satisfying: L ( s , ρ , L / K ) = L ( s , π )
Artin_L-function
Discrete subgroup in a locally compact topological group
number field F {\displaystyle F} and A {\displaystyle \mathbb {A} } its adèle ring then the group G = G ( A ) {\displaystyle G=\mathrm {G} (\mathbb {A} )}
Lattice_(discrete_subgroup)
On the reciprocity law in algebraic number fields
Galois group of this extension and A K {\displaystyle \mathbf {A} _{K}} be adele ring of K {\displaystyle K} . If L ( s , ρ , L / K ) {\displaystyle L(s,\rho
Hilbert's_ninth_problem
2011 song by Adele
singer-songwriter Adele for her second studio album, 21 (2011). The song was written by Adele and Ryan Tedder; the latter is also the producer. Adele has stated
Rumour_Has_It_(Adele_song)
Number system extending the rational numbers
which are seen as encoding "local" information. This is accomplished by adele rings and idele groups. p-adic integers can be extended to p-adic solenoids
P-adic_number
2016 American film
Dora's death, which Adele only learns about when the food tray remains untouched. Upon discovering the body, Adele takes a ring with a greenish stone
Sweet,_Sweet_Lonely_Girl
locally constant function of compact support. In particular, on the ring of adeles A K {\displaystyle \mathbb {A} _{K}} over a global field K {\displaystyle
Schwartz–Bruhat_function
Number-theoretic concept
is the ring of p-adic integers. This group is important because of its relation to Galois theory, étale homotopy theory, and the ring of adeles. In addition
Profinite_integer
Irish entertainer (born 1951)
Adèle King (born Adèle Condron-King, 4 April 1951) is an Irish entertainer better known as Twink. She is from Dublin. She is the mother of singer Chloë
Adele_King
Group that is also a differentiable manifold with group operations that are smooth
modern number theory, deals extensively with analogues of Lie groups over adele rings; p-adic Lie groups play an important role, via their connections with
Lie_group
Mathematical group
{R} } . (It has analogues over other local fields, finite fields, and adele rings.) Hamiltonian mechanics Metaplectic group Orthogonal group Paramodular
Symplectic_group
American sports agent (born 1980)
2023. Murphy, Nichola (February 28, 2023). "Everything Adele has said about £750k engagement ring and secret Rich Paul wedding plans". Hello Magazine. Retrieved
Rich_Paul
American writer (1885–1933)
Vincent Youmans—with whom he toiled on the Ziegfeld–Marilyn Miller–Fred and Adele Astaire musical Smiles (1930). Lardner's books were published by Maxwell
Ring_Lardner
2001 film by Frank Darabont
Doc's daughter, Adele. Hesitantly, Peter accepts being treated as Luke by the townspeople, led by Mayor Ernie Cole, and gets to know Adele, who had been
The_Majestic_(film)
correcting an error of Grunwald's. 1950 Tate's thesis uses analysis on adele rings to study zeta functions. 1951 André Weil introduces Weil groups. 1952
Timeline of class field theory
Timeline_of_class_field_theory
List of television series episodes
2 Episodes No. overall No. in season Title Original release date 15 1 "Adele Craven" February 20, 2005 (2005-02-20) When a successful airline pilot and
List_of_Snapped_episodes
Belgium fine artist
Adele Renault is a visual artist and muralist, known for her hyper- and photo-realistic paintings from smaller works on canvas and large-scale public
Adele_Renault
1991 single by Bonnie Raitt
"both seem deeply heartfelt, like Adele understands, and is the only one who can make these words that are not hers ring true." Chris Willman of The Wrap
I_Can't_Make_You_Love_Me
English-born Scottish actor (born 1990)
Shailene Woodley (2012) Jeremy Irvine / Blanca Suárez (2013) Logan Lerman / Adèle Exarchopoulos (2014) Jack O'Connell / Lola Kirke (2015) John Boyega / Bel
Jack_Lowden
Doughnut-shaped surface of revolution
coplanar with the circle. The main types of tori include ring tori, horn tori, and spindle tori. A ring torus is sometimes colloquially referred to as a doughnut
Torus
Kesslering Brylee Jeffries Harper Doige Kaylee Rosenfelt Yorkton, Saskatchewan Adele Kezama-Purcell Deanne Nichol Meghan Chateauvert Heather Steele St. Albert
List of teams in the 2021–22 curling season
List_of_teams_in_the_2021–22_curling_season
Country in Northwestern Europe
Coldplay, Arctic Monkeys, Robbie Williams, Amy Winehouse, Susan Boyle, Adele, Ed Sheeran, Lewis Capaldi, One Direction, Harry Styles and Dua Lipa. As
United_Kingdom
American singer and actress (born 1992)
"The Decade in Charts: Mark & Bruno's 'Uptown Funk!' Rules Hot 100 & Adele's '21' Tops Billboard 200". Billboard. Retrieved April 20, 2024. "Decade-End
Miley_Cyrus
Species of bird
distributed of all penguins. It is named after Adélie Land, in turn, named for Adèle Dumont d'Urville, who was married to French explorer Jules Dumont d'Urville
Adélie_penguin
German-Jewish concert promoter (born 1946)
the Rock am Ring and Rock im Park festivals ceased in 2022, after he served as head of the organisers. In 2024, Lieberberg co-promoted Adele in Munich.
Marek_Lieberberg
Margaret Davies 1985 1992 HN2479 Pamela Margaret Davies 1986 1994 HN2480 Adele Margaret Davies 1987 1992 HN2481 Maureen Margaret Davies 1987 1992 HN2482
List of Royal Doulton figurines
List_of_Royal_Doulton_figurines
American singer and songwriter (1958–2009)
February 16, 2017. Retrieved May 31, 2015. Crookes, Del (May 4, 2012). "Adele's 21 overtakes sales of Thriller in UK album list". Newsbeat. Archived from
Michael_Jackson
New Zealand singer-songwriter (born 1996)
February 2014, becoming the first debut album by a female artist since Adele's 19 (2008) to achieve the feat. Pure Heroine earned a Grammy nomination
Lorde
French singer and musician (1957–2026)
2007: La tête de maman 2009: Korkoro 2010: The Extraordinary Adventures of Adèle Blanc-Sec 2022: Les Cadors 1969: Les Deux Coquines (Kiki) 1976: La Fessée
Catherine_Ringer
(eigenfunction expansions) Paul Jaffard, Anneaux d'adèles d'après Iwasawa (adele rings) André Néron, Variétés abéliennes, d'après A. Weil (en introduction à
Séminaire Nicolas Bourbaki (1950–1959)
Séminaire_Nicolas_Bourbaki_(1950–1959)
American professional wrestler (1953–2025)
Bollea (/bəˈleɪə/; August 11, 1953 – July 24, 2025), better known by his ring name Hulk Hogan, was an American professional wrestler and media personality
Hulk_Hogan
First electronic general-purpose digital computer
Clippinger, Adele Goldstine and others. It was first demonstrated as a stored-program computer in April 1948, running a program by Adele Goldstine for
ENIAC
Annual popular music award
producer, engineer and songwriter can apply for a Winners Certificate. Adele has the most victories (with four wins), and is the only act so far to win
Grammy Award for Best Pop Solo Performance
Grammy_Award_for_Best_Pop_Solo_Performance
British actress and singer (1908–1992)
Adele Dixon (born Adelaide Helena Dixon; 3 June 1908 – 11 April 1992) was an English actress and singer. She sang at the start of regular broadcasts of
Adele_Dixon
German and Irish actor (born 1977)
Heidelberg, a city in the West German state of Baden-Württemberg. His mother, Adele, is originally from Larne, Northern Ireland, and his father, Josef Fassbender
Michael_Fassbender
2009 American TV series or program
as Michael "Mike" Trainor Daryl Mitchell as Chill Trainor CCH Pounder as Adele Trainor Carl Weathers as Coach Trainor Every episode of the series was directed
Brothers_(2009_TV_series)
Japanese swordsman, strategist, writer, artist, and rōnin (c. 1584–1645)
of swordsmanship. In his final years, Musashi authored The Book of Five Rings (五輪の書, Go Rin No Sho) and Dokkōdō (獨行道, The Path of Aloneness). Both documents
Miyamoto_Musashi
Next Film; Taps All-Star Cast With Nicholas Hoult, Aaron Taylor-Johnson, Adele, Owen Cooper & More". Deadline Hollywood. Archived from the original on
List of Ciarán Hinds performances
List_of_Ciarán_Hinds_performances
English rock band (1960–1970)
a bright, joyous, original sound, filled with ringing guitars and irresistible melodies." That "ringing guitar" sound was primarily the product of Harrison's
The_Beatles
American singer, songwriter, and actress (born 1993)
Victorious, Grande made several recordings of herself singing covers of songs by Adele, Whitney Houston, and Mariah Carey and uploaded them to YouTube. A friend
Ariana_Grande
Awards); to Per Hallberg and Karen Baker Landers for Sound Editing and to Adele and Paul Epworth for Original Song in Skyfall (at the 85th Awards); to Sam
List_of_James_Bond_films
2018 film by Jon M. Chu
drama film directed by Jon M. Chu from a screenplay by Peter Chiarelli and Adele Lim, based on the 2013 novel by Kevin Kwan. The film stars Constance Wu
Crazy_Rich_Asians
American superhero media franchise
from the original on May 8, 2024. Retrieved May 8, 2024. Ankers-Range, Adele (May 22, 2024). "Marvel's What If...? – An Immersive Story for Apple Vision
Marvel_Cinematic_Universe
July 12, 2024. Jaafar, Ali (August 24, 2015). "A24 Teams with Plan B & Adele Romanski to Produce and Finance Barry Jenkins' Moonlight". Deadline Hollywood
List_of_A24_films
1968 film
disrupting the routines. Heinz Rühmann as Dr. Alexander Hertha Feiler as Adele Graziella Granata as Dr Jaspers Charles Regnier as Professor Sauermann John
The Duck Rings at Half Past Seven
The_Duck_Rings_at_Half_Past_Seven
Swedish violinist and conductor (1897–1989)
as Bobby). They divorced in 1928. His second wife was Australian actress Adele Crane, whom he married in 1929. This marriage lasted until 1939 and also
Jan_Rubini
2024 wedding in Mumbai, India
CEO Amin H Nasser, American politician John Kerry, and celebrities like Adele, David Beckham, John Cena and the Kardashians. Some Indian politicians criticised
Wedding of Anant Ambani and Radhika Merchant
Wedding_of_Anant_Ambani_and_Radhika_Merchant
French religious sister
Adèle de Batz de Trenquelléon, FMI, religious name Mary of the Conception (French: Marie de la Conception), (10 June 1789 – 10 January 1828), was a religious
Adèle_de_Batz_de_Trenquelléon
American actor and filmmaker (born 1946)
Retrieved September 20, 2026. "Cedars-Sinai Board Of Governors Gala To Honor Adele & Beny Alagem and Sylvester Stallone". The Beverly Hills Courier. October
Sylvester_Stallone
Dessert: cherries, pumpernickel bread, curry powder, yuzu juice Contestants: Adele DiBiase, Chef and Restaurateur, Bona Vita Osteria, Summit, NJ (eliminated
List of Chopped episodes (seasons 1–20)
List_of_Chopped_episodes_(seasons_1–20)
Country in Eastern Europe and North Asia
Andreas (12 July 2010). ""Great Russians" and '"Little Russians"". In Barker, Adele Marie; Grant, Bruce (eds.). The Russia Reader: History, Culture, Politics
Russia
Video game award
original on December 10, 2020. Retrieved November 15, 2022. Ankers-Range, Adele (November 17, 2021). "The Game Awards Nominations Announced". IGN. Ziff
The Game Award for Game of the Year
The_Game_Award_for_Game_of_the_Year
Performances by American dancer and musician
Smiles Nov. 18 1930 Ziegfeld Bob Hastings Adele Astaire Marilyn Miller William Anthony McGuire Clifford Grey Harold Adamson Ring Lardner Vincent Youmans
Fred Astaire chronology of performances
Fred_Astaire_chronology_of_performances
Polish boxer (born 1979)
Świebodzice, Poland. He made his American debut in January 2006 by defeating Adele Olakanye by decision on the undercard of Arturo Gatti's destruction of Thomas
Mariusz_Wach
American singer-songwriter (born 1985)
Kimpel, Dan (March 7, 2016). "Songwriter Profile: Body Brown (Bruno Mars, Adele, Mark Ronson)". Music Connection. Archived from the original on November
Bruno_Mars
English musician and songwriter (born 1942)
2010. Casciato, Paul (11 April 2013). "McCartney tops UK music rich list, Adele richest youngster". Reuters. Archived from the original on 4 June 2013.
Paul_McCartney
American actress and singer (born 1997)
18, 2016. Romano, Nick (March 13, 2016). "Star Wars: The Force Awakens, Adele, more win big at 2016 Kids' Choice Awards". Entertainment Weekly. Retrieved
Kira_Kosarin
American actress and model
in Cincinnati and named after the character Galadriel in The Lord of the Rings, which her mother read while pregnant. She graduated from Newport Central
Galadriel_Stineman
American actress (born 1959)
include Final Jeopardy (1985) and Stagecoach (1986). In 1987, she starred as Adele Strauss in the German biographical film Johann Strauss - Der König ohne
Mary_Crosby
Italian actress (1917–2003)
Ring Around the Clock (1950) – Concettina Strano appuntamento (1950) The Steamship Owner (1951) – one of the furious women Perdonami! (1953) – Adele Passionate
Zoe_Incrocci
2023 film by Scott Waugh
Expendables for contract work. Additionally, Sheila Shah was cast as Mandy / Adele, alongside Daren Nop as Bok, Rahmats right hand man, and Eddie Hall as a
Expend4bles
American writer (1923–2007)
of assault and served a three-year probation after he stabbed his wife Adele Morales with a penknife, nearly killing her. In 1969, he ran an unsuccessful
Norman_Mailer
Actress (born 1996)
Retrieved 8 October 2025. Warner Bros. (14 July 2026). The Lord of the Rings: The Hunt for Gollum | Start of Production. Archived from the original on
Anya_Taylor-Joy
Sexual abuse scandal in England
ISBN 9781509801619. Weir, Adele (23 October 2001). "Letter" (PDF). London: House of Commons, The Stationery Office Ltd. Weir, Adele (2002). "Chapter Four:
Rotherham child sexual exploitation scandal
Rotherham_child_sexual_exploitation_scandal
2025 American television series
Shores School. She gets fired in "Summer of Secrets". Katrina Reynolds as Adele, Jinx's mother Toby Berner as Randy, Kombucha's father Tony Alcantar as
The_Thundermans:_Undercover
Largest city in Texas, United States
from the original on April 12, 2018. Retrieved April 12, 2018. Looscan, Adele B. (1914). "Harris County, 1822–1845". Southwestern Historical Quarterly
Houston
List of episodes of the British TV drama series
Little Upton. Barnaby and Winter learn later on that Naomi and her friend Adele Paige ran the Old Vogue Vintage Emporium together. A reporter starts to
List of Midsomer Murders episodes
List_of_Midsomer_Murders_episodes
2023 film by Laura Terruso
respected Sicilian-American hairstylist, for his late grandmother's wedding ring. Salvo agrees on the condition that he meet Ellie's parents first. Sebastian
About_My_Father
American actress (born 1990)
series Poker Face, which was released in 2023. Later in 2023, she starred in Adele Lim's film Joy Ride. She appeared in an episode of the Disney+ series American
Stephanie_Hsu
travel, tourism, insurance
ADELE RING
ADELE RING
Girl/Female
American, German
Noble; Kind
Girl/Female
German Hebrew
from the Old German 'athal' meaning noble.
Girl/Female
German, Greek, Hebrew
Rich; Harmonious; Song; I will Praise the Lord
Girl/Female
French American German
Good humor; Of the nobility. Noble.
Boy/Male
Indian
Judge, Honest, Upright, Justice, Sincere, Just
Female
English
Latin form of German Adala, ADELA means "noble." In use by the Danish and Swedish.
Female
English
French form of German Adala, ADELLE means "noble."
Girl/Female
Afghan, American, British, Christian, English, Finnish, French, German, Indian, Kannada, Latin, Polish, Swedish
Nobility; Noble Kind; Softer; Small Winged One
Female
English
Variant spelling of English Adena, ADENE means "fire."
Girl/Female
American, Bengali, Christian, German, Indian
Noble; Form of Adelaide; Noble and of Kind Spirit
Girl/Female
Greek
Harmonious.
Girl/Female
German American French
Sweet or noble.
Girl/Female
Arabic, Indian, Kannada, Muslim
Equal; Derived from Adeline
Boy/Male
Muslim
Judge, Honest, Upright, Justice, Sincere, Just
Girl/Female
American, Australian, British, Christian, English, German, Swedish, Teutonic
Nobility; Noble Kind; Soft; Sweet
Female
African
famous.
Girl/Female
Anglo, British, English, German
Wealthy
Male
Italian
Italian form of Hebrew Hebel, ABELE means "breath, breathing."
Female
English
English form of French Adèle, ADELE means "noble sort."
Girl/Female
Latin American French German
Of the nobility. Noble.
ADELE RING
ADELE RING
ADELE RING
ADELE RING
ADELE RING
ADELE RING
ADELE RING
travel, tourism, insurance