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Concept in number theory
In mathematics, the adele ring is a construction in number theory that combines all local versions of a global field into one object. For the rational
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
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
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)
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
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)
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
{\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)
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
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)
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
American singer 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
(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)
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
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
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
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
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
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
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
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)
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
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
American singer and actress (born 1969)
Keith (May 11, 2011). "Beastie Boys Score No. 2 Debut on Billboard 200, Adele Holds at No. 1". Billboard. Archived from the original on December 26, 2021
Jennifer_Lopez
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
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
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 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
German-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
English musician, songwriter and activist (1940–1980)
2010s Fearless – Taylor Swift (2010) The Suburbs – Arcade Fire (2011) 21 – Adele (2012) Babel – Mumford & Sons (2013) Random Access Memories – Daft Punk
John_Lennon
English musician (1943–2001)
2010s Fearless – Taylor Swift (2010) The Suburbs – Arcade Fire (2011) 21 – Adele (2012) Babel – Mumford & Sons (2013) Random Access Memories – Daft Punk
George_Harrison
American actor (born 1954)
made headlines for mispronouncing the name of Idina Menzel by calling her "Adele Dazeem" during the live broadcast of the 86th Academy Awards; he subsequently
John_Travolta
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
President of the United States in 1881
run the mail routes would be escalated and profits would be divided among ring members. Shortly after taking office, Garfield received word of postal corruption
James_A._Garfield
American singer and songwriter (born 1981)
Love", "Baby Boy", "Check on It", "Irreplaceable", and "Single Ladies (Put a Ring on It)". After forming the management company Parkwood Entertainment, Beyoncé
Beyoncé
American singer and songwriter (born 1966)
Ebony, vol. 46, no. 10, p. 40, ISSN 0012-9011 Eng, Joyce (May 21, 2012). "Adele, LMFAO Top Billboard Music Awards – Today's News: Our Take". TV Guide. Archived
Janet_Jackson
American businessman and actor (born 1975)
July 10, 2012. Retrieved July 10, 2012. "Sofia Vergara Engaged, Shows Off Ring During Birthday Celebration". E!. July 10, 2012. Retrieved July 10, 2012
Nick_Loeb
(October 4, 2024). "Disney's Princess Diaries 3 Gets Royal Treatment, Sets Adele Lim As Director". Deadline Hollywood. Retrieved October 4, 2024. Kroll,
List of Walt Disney Studios films (2020–2029)
List_of_Walt_Disney_Studios_films_(2020–2029)
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-songwriter (born 1941)
songs and "Make You Feel My Love" was covered by Billy Joel, Garth Brooks, Adele and others. Elvis Costello said "I think it might be the best record he's
Bob_Dylan
2023 concert tour by Beyoncé
Duchess of Sussex, Diana Ross, Katy Perry and Kim Kardashian. British singer Adele said that she stayed up until 3 am buying metallic clothing on Amazon for
Renaissance_World_Tour
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
back-to-back Tarr, Tanya (September 16, 2019). "Here's What We Learn From Watching Adele Lim Walk Away From The Pay Gap". Forbes. Archived from the original on December
List of Warner Bros. films (2020–2029)
List_of_Warner_Bros._films_(2020–2029)
University of Maryland, College Park † MPC · 12517 12519 Pullen 1998 HH55 Sarah Adele Pullen (born 1985), an ISEF awardee in 2002 JPL · 12519 12522 Rara 1998
Meanings of minor-planet names: 12001–13000
Meanings_of_minor-planet_names:_12001–13000
Capital of France
encouraging walking and cycling?". Euronews. Retrieved 4 April 2025. Peters, Adele (9 May 2024). "How Paris became a 15-minute city". Fast Company. Retrieved
Paris
American actress (born 1990)
Poker Face, which was released in 2023. Later that year, Hsu starred in Adele Lim's film Joy Ride. She also appeared in an episode of the Disney+ series
Stephanie_Hsu
Japanese swordsman, strategist, writer, artist, and rōnin (c. 1584–1645)
the Geisha. Broadway Books. ISBN 978-0767904902. Ratti, Oscar; Westbrook, Adele (2011). Secrets of the Samurai: The Martial Arts of Feudal Japan. Tuttle
Miyamoto_Musashi
American rapper and singer (born 1998)
leading up to the release of Pray 4 Love, Green cited Tupac Shakur and Adele as two of his inspirations, noting that he can "hear everything she went
Rod_Wave
German-Austrian actress (1945–2017)
Heiter bis tödlich – Fuchs und Gans Diana Bootz "Eierdiebe" 2013 Stille [de] Adele Vio TV film 2013 Tiere bis unters Dach Frau von Werther "Die Millionenkatze"
Christine_Kaufmann
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
American singer and actor (1915–1998)
sold it for an estimated $80 million. Sinatra's first album on the label, Ring-a-Ding-Ding! (1961), was a major success, peaking at No.4 on Billboard. The
Frank_Sinatra
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
2012 death of American singer and actress
Album Chart at this time. Houston also became the second female act, after Adele, to place two albums in the top five of the US Billboard Top 200, with Whitney:
Death_of_Whitney_Houston
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
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
ADELE RING
ADELE RING
Girl/Female
German American French
Sweet or noble.
Girl/Female
Anglo, British, English, German
Wealthy
Girl/Female
German, Greek, Hebrew
Rich; Harmonious; Song; I will Praise the Lord
Boy/Male
Indian
Judge, Honest, Upright, Justice, Sincere, Just
Girl/Female
French American German
Good humor; Of the nobility. Noble.
Female
English
English form of French Adèle, ADELE means "noble sort."
Girl/Female
Afghan, American, British, Christian, English, Finnish, French, German, Indian, Kannada, Latin, Polish, Swedish
Nobility; Noble Kind; Softer; Small Winged One
Girl/Female
Arabic, Indian, Kannada, Muslim
Equal; Derived from Adeline
Male
Italian
Italian form of Hebrew Hebel, ABELE means "breath, breathing."
Female
English
French form of German Adala, ADELLE means "noble."
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
Girl/Female
Greek
Harmonious.
Girl/Female
American, German
Noble; Kind
Girl/Female
German Hebrew
from the Old German 'athal' meaning noble.
Boy/Male
Muslim
Judge, Honest, Upright, Justice, Sincere, Just
Female
English
Variant spelling of English Adena, ADENE means "fire."
Female
African
famous.
Female
English
Latin form of German Adala, ADELA means "noble." In use by the Danish and Swedish.
Girl/Female
American, Bengali, Christian, German, Indian
Noble; Form of Adelaide; Noble and of Kind Spirit
ADELE RING
ADELE RING
Surname or Lastname
English
English : habitational name from Parnham in Beaminster, Dorset.
Boy/Male
Hebrew
Independence.
Boy/Male
German
Friend.
Male
Egyptian
, land of gold.
Boy/Male
Muslim/Islamic
Reminder
Boy/Male
Indian
Harmony
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit
Draupadi's Name
Boy/Male
Hindu, Indian, Marathi
Brave Person
Girl/Female
Indian, Punjabi, Sikh
Absorbed in Devotion; Pray to God from the Heart
Male
Finnish
Finnish form of Greek Elias, ELJAS means "the Lord is my God."Â
ADELE RING
ADELE RING
ADELE RING
ADELE RING
ADELE RING
v. t.
To earn. [Obs.] See Addle, to earn.
v. t.
To give extreme unction to.
n.
The white poplar (Populus alba).
a.
Alt. of Addle-pated
v. t.
To blot out; to erase; to expunge; to dele; to omit.
n.
Lees; dregs.
p. pr. & vb. n.
of Dele
v. t. & i.
To make addle; to grow addle; to muddle; as, he addled his brain.
v. t. & i.
To earn by labor.
a.
Having lost the power of development, and become rotten, as eggs; putrid. Hence: Unfruitful or confused, as brains; muddled.
n.
Alt. of Addle-pate
v. t.
To deal; to divide; to distribute.
p. pr. & vb. n.
of Addle
imp. & p. p.
of Addle
n.
Alt. of Addle-pate
v. t. & i.
To thrive or grow; to ripen.
a.
Alt. of Addle-pated
imp. & p. p.
of Dele
n.
Liquid filth; mire.
v. t.
To anoint.