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- Tates_thesis abstract "In number theory, Tate's thesis is the 1950 thesis of John Tate (1950) under supervision of Emil Artin. In it, he used a translation invariant integration on the locally compact group of ideles to lift the zeta function of a number field, twisted by a Hecke character, to a zeta integral and study its properties. Using harmonic analysis, more precisely the summation formula, he proved the functional equation and meromorphic continuation of the zeta integral and the twisted zeta function. He also located the poles of the twisted zeta function. His work can be viewed as an elegant and powerful reformulation of a work of Erich Hecke on the proof of the functional equation of the twisted zeta function (L-function). Hecke used a generalized theta series associated to an algebraic number field and a lattice in its ring of integers. Kenkichi Iwasawa independently discovered during the war essentially the same method (without an analog of the local theory in Tate's thesis) and announced it in his 1950 ICM paper and his letter to Dieudonné written in 1952. Hence this theory is often called Iwasawa–Tate theory. Iwasawa in his letter to Dieudonné derived on several pages not only the meromorphic continuation and functional equation of the L-function, he also proved finiteness of the class number and Dirichlet's theorem on units as immediate byproducts of the main computation. The theory in positive characteristic was developed one decade earlier by Witt, Schmid and Teichmuller. Iwasawa-Tate theory uses several structures which come from class field theory, however it does not use any deep result of class field theory.".
- Tates_thesis wikiPageExternalLink ICM1950.1.
- Tates_thesis wikiPageExternalLink books?ei=jyALTq-_L4nkiAL6zrHXAQ.
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- Tates_thesis wikiPageID "3149490".
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- Tates_thesis wikiPageRevisionID "695645827".
- Tates_thesis wikiPageWikiLink Adelic_algebraic_group.
- Tates_thesis wikiPageWikiLink American_Mathematical_Society.
- Tates_thesis wikiPageWikiLink Arithmetic_zeta_function.
- Tates_thesis wikiPageWikiLink Category:1950_in_science.
- Tates_thesis wikiPageWikiLink Category:1950_works.
- Tates_thesis wikiPageWikiLink Category:Algebraic_number_theory.
- Tates_thesis wikiPageWikiLink Category:Zeta_and_L-functions.
- Tates_thesis wikiPageWikiLink Class_field_theory.
- Tates_thesis wikiPageWikiLink Emil_Artin.
- Tates_thesis wikiPageWikiLink Erich_Hecke.
- Tates_thesis wikiPageWikiLink Field_(mathematics).
- Tates_thesis wikiPageWikiLink Harmonic_analysis.
- Tates_thesis wikiPageWikiLink Hervé_Jacquet.
- Tates_thesis wikiPageWikiLink Ivan_Fesenko.
- Tates_thesis wikiPageWikiLink Kenkichi_Iwasawa.
- Tates_thesis wikiPageWikiLink Langlands_program.
- Tates_thesis wikiPageWikiLink List_of_zeta_functions.
- Tates_thesis wikiPageWikiLink Number_theory.
- Tates_thesis wikiPageWikiLink Roger_Godement.
- Tates_thesis wikiPageWikiLinkText "Tate's thesis".
- Tates_thesis authorlink "John Tate".
- Tates_thesis first "John".
- Tates_thesis last "Tate".
- Tates_thesis wikiPageUsesTemplate Template:Citation.
- Tates_thesis wikiPageUsesTemplate Template:Cite_book.
- Tates_thesis wikiPageUsesTemplate Template:Harvs.
- Tates_thesis year "1950".
- Tates_thesis subject Category:1950_in_science.
- Tates_thesis subject Category:1950_works.
- Tates_thesis subject Category:Algebraic_number_theory.
- Tates_thesis subject Category:Zeta_and_L-functions.
- Tates_thesis hypernym Thesis.
- Tates_thesis type Book.
- Tates_thesis type Work.
- Tates_thesis type Function.
- Tates_thesis type Work.
- Tates_thesis comment "In number theory, Tate's thesis is the 1950 thesis of John Tate (1950) under supervision of Emil Artin. In it, he used a translation invariant integration on the locally compact group of ideles to lift the zeta function of a number field, twisted by a Hecke character, to a zeta integral and study its properties. Using harmonic analysis, more precisely the summation formula, he proved the functional equation and meromorphic continuation of the zeta integral and the twisted zeta function.".
- Tates_thesis label "Tate's thesis".
- Tates_thesis sameAs Q7687933.
- Tates_thesis sameAs テイト論文.
- Tates_thesis sameAs m.0gy1gt9.
- Tates_thesis sameAs Q7687933.
- Tates_thesis wasDerivedFrom Tates_thesis?oldid=695645827.
- Tates_thesis isPrimaryTopicOf Tates_thesis.