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- Tate's_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.".
- Tate's_thesis wikiPageExternalLink books?ei=jyALTq-_L4nkiAL6zrHXAQ.
- Tate's_thesis wikiPageExternalLink books?id=x3XR0ljIV6YC.
- Tate's_thesis wikiPageExternalLink ICM1950.1.
- Tate's_thesis wikiPageID "3149490".
- Tate's_thesis wikiPageRevisionID "591968296".
- Tate's_thesis authorlink "John Tate".
- Tate's_thesis first "John".
- Tate's_thesis hasPhotoCollection Tate's_thesis.
- Tate's_thesis last "Tate".
- Tate's_thesis year "1950".
- Tate's_thesis subject Category:1950_in_science.
- Tate's_thesis subject Category:1950_works.
- Tate's_thesis subject Category:Algebraic_number_theory.
- Tate's_thesis subject Category:Zeta_and_L-functions.
- Tate's_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.".
- Tate's_thesis label "Tate's thesis".
- Tate's_thesis sameAs m.0gy1gt9.
- Tate's_thesis sameAs Q7687933.
- Tate's_thesis sameAs Q7687933.
- Tate's_thesis wasDerivedFrom Tate's_thesis?oldid=591968296.
- Tate's_thesis isPrimaryTopicOf Tate's_thesis.