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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
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
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
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)
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
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
English singer-songwriter (born 1988)
Adele Laurie Blue Adkins (/əˈdɛl/ ə-DEL; born 5 May 1988), known mononymously as Adele, is an English singer and songwriter. Regarded as a British cultural
Adele
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)
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
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
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
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 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
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)
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
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
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)
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
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
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
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
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
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
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
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
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)
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
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
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
{\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
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)
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 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
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
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
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)
Mathematical group
{R} } . (It has analogues over other local fields, finite fields, and adele rings.) Hamiltonian mechanics Metaplectic group Orthogonal group Paramodular
Symplectic_group
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
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
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
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
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
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
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)
2023 film by Christopher Nolan
the original on July 3, 2023. Retrieved August 11, 2023. Ankers-Range, Adele (June 30, 2023). "The Internet Embraces 'Barbenheimer' With Memes, Mashups
Oppenheimer_(film)
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
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
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
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
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
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
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 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
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 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
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
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
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
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
Country in West Africa
of the Adele plateau. Most Ntrubo communities, however, live in Ghana, just west of this area. In Togo, the Ntrubo coexist closely with the Adele, speaking
Togo
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
Retired British TV executive (born 1954)
. with Jools Holland, One Love Manchester, the Royal Opera and Ballet, Adele at the BBC and Imagine... This House is Full of Music with the Kanneh-Mason
Jan_Younghusband
German and Irish actor (born 1977)
Heidelberg, a city in the West German state of Baden-Württemberg. His mother, Adele, is originally from Larne, County Antrim, Northern Ireland, and his father
Michael_Fassbender
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
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
co-production Danger: Mother-in-Law! [de] Zoltan Spirandelli Katharina Schüttler, Adele Neuhauser, Arne Lenk [de] Comedy a.k.a. Vorsicht Schwiegermutter! The Day
List of German films of the 2000s
List_of_German_films_of_the_2000s
American singer (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
American and British internet personality (born 1986)
Boxing Scene. Nandy, Anisa (16 October 2025). "Andrew Tate to step into the ring for the first time against Chase DeMoor at Misfits 23". Primetimer. Archived
Andrew_Tate
American actress (born 1948)
Polish Jewish immigrant who was a manager at a doll parts factory, and Adele Perlman, a bookkeeper. She grew up in nearby Bensonhurst in a Jewish family
Rhea_Perlman
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
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
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
American singer and drummer (1950–1983)
Bangles, Debbie Gibson, Taylor Swift, Beyonce, Gloria Estefan, Mandy Moore, Adele, Alison Krauss, Clairo, The Corrs, Rumer, Norah Jones, Linda Perry, Michael
Karen_Carpenter
English singer (born 2003)
as a formative influence on her music. She has also named Amy Winehouse, Adele, Bob Marley, and Eminem among her musical inspirations. Headlining The Woman
Skye_Newman
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
2025 Marvel Studios film
the original on March 27, 2024. Retrieved March 27, 2024. Ankers-Range, Adele (April 12, 2024). "Marvel Fans Are Trying to Figure Out Why Thunderbolts
Thunderbolts*
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 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
2022 American gothic horror television series
shows to watch if you liked 'House of the Dragon' and 'The Lord of the Rings: The Rings of Power'". Mashable. November 6, 2022. Archived from the original
Interview with the Vampire (TV series)
Interview_with_the_Vampire_(TV_series)
2024 Marvel Studios film
original on February 9, 2023. Retrieved February 9, 2023. Ankers-Range, Adele (August 8, 2024). "Deadpool & Wolverine Director Says a Patrick Stewart
Deadpool_&_Wolverine
Swedish musician and composer (born 1984)
of the Year). He has also produced for other recording artists, such as Adele, Alicia Keys, Rihanna, Chance the Rapper, Haim, Justin Timberlake, Kendrick
Ludwig_Göransson
2025 American TV series
Norton & Company. pp. 3–5. ISBN 0393048039. Coogan 2010, p. 784 Berlin, Adele; Brettler, Marc Zvi, eds. (2004). The Jewish Study Bible. Oxford University
House_of_David_(TV_series)
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
American actor (born 1939)
Doors to Syrians". The New York Times. Retrieved June 1, 2021. Obituary of Adele Hendricks Abraham (1923–2019), aunt of Murray Abraham, where it is stated
F._Murray_Abraham
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
American actor and filmmaker (born 1946)
Retrieved January 16, 2025. "Cedars-Sinai Board Of Governors Gala To Honor Adele & Beny Alagem and Sylvester Stallone". The Beverly Hills Courier. October
Sylvester_Stallone
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
2019 film
film written and directed by Quentin Dupieux. It stars Jean Dujardin and Adèle Haenel. In the film, Georges (Dujardin) becomes obsessive after purchasing
Deerskin_(film)
American singer-songwriter (1939–2026)
Retrieved January 26, 2018. Curt Schleier (June 7, 2012). "Q&A: Neil Sedaka on Adele and Carole King – The Arty Semite – Forward.com". The Forward. Archived
Neil_Sedaka
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
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
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
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
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
(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 musician (born 1986)
2010s Fearless – Taylor Swift (2010) The Suburbs – Arcade Fire (2011) 21 – Adele (2012) Babel – Mumford & Sons (2013) Random Access Memories – Daft Punk
Jon_Batiste
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
Disc-shaped analog sound storage medium
skiva Black-star. Andra populära artister är Beatles, Led Zeppelin och Adele." – or in English – "More and more buy vinyl records. The trend to buy vinyl
Phonograph_record
ADELE RING
ADELE RING
Girl/Female
Afghan, American, British, Christian, English, Finnish, French, German, Indian, Kannada, Latin, Polish, Swedish
Nobility; Noble Kind; Softer; Small Winged One
Girl/Female
German, Greek, Hebrew
Rich; Harmonious; Song; I will Praise the Lord
Boy/Male
Indian
Judge, Honest, Upright, Justice, Sincere, Just
Girl/Female
American, German
Noble; Kind
Female
English
English form of French Adèle, ADELE means "noble sort."
Female
English
Variant spelling of English Adena, ADENE means "fire."
Girl/Female
German Hebrew
from the Old German 'athal' meaning noble.
Boy/Male
Muslim
Judge, Honest, Upright, Justice, Sincere, Just
Male
Italian
Italian form of Hebrew Hebel, ABELE means "breath, breathing."
Girl/Female
French American German
Good humor; Of the nobility. Noble.
Girl/Female
German American French
Sweet or noble.
Girl/Female
Greek
Harmonious.
Girl/Female
Anglo, British, English, German
Wealthy
Girl/Female
Latin American French German
Of the nobility. Noble.
Girl/Female
American, Australian, British, Christian, English, German, Swedish, Teutonic
Nobility; Noble Kind; Soft; Sweet
Female
English
Latin form of German Adala, ADELA means "noble." In use by the Danish and Swedish.
Girl/Female
Arabic, Indian, Kannada, Muslim
Equal; Derived from Adeline
Female
English
French form of German Adala, ADELLE means "noble."
Girl/Female
American, Bengali, Christian, German, Indian
Noble; Form of Adelaide; Noble and of Kind Spirit
Female
African
famous.
ADELE RING
ADELE RING
Boy/Male
Biblical
Bitterness, rebellious, changing.
Girl/Female
Biblical
My God judgeth.
Male
Norse
Contracted form of Old Norse Hróðgeirr, HRÓARR means "famous spear."
Female
English
Variant spelling of English Rhonda, RONDA means "noisy."Â
Girl/Female
Arabic, Muslim
Easy; Convenient
Girl/Female
Hebrew American Spanish
Innocent.
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Moon
Boy/Male
Hindu, Indian
Meteor
Girl/Female
Tamil
Deepaprabha | தீபபà¯à®°à®ªà®¾
Fully lighted
Girl/Female
Arabic
Beautiful
ADELE RING
ADELE RING
ADELE RING
ADELE RING
ADELE RING
v. t.
To deal; to divide; to distribute.
a.
Alt. of Addle-pated
n.
Alt. of Addle-pate
a.
Having lost the power of development, and become rotten, as eggs; putrid. Hence: Unfruitful or confused, as brains; muddled.
p. pr. & vb. n.
of Dele
v. t. & i.
To earn by labor.
imp. & p. p.
of Addle
n.
Lees; dregs.
p. pr. & vb. n.
of Addle
a.
Alt. of Addle-pated
v. t.
To give extreme unction to.
n.
Liquid filth; mire.
n.
Alt. of Addle-pate
imp. & p. p.
of Dele
v. t. & i.
To make addle; to grow addle; to muddle; as, he addled his brain.
n.
The white poplar (Populus alba).
v. t.
To earn. [Obs.] See Addle, to earn.
v. t.
To anoint.
v. t. & i.
To thrive or grow; to ripen.
v. t.
To blot out; to erase; to expunge; to dele; to omit.