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Tate's thesis, the Glossary

In number theory, Tate's thesis is the 1950 PhD thesis of completed under the supervision of Emil Artin at Princeton University.^[1]

29 relations: Adelic algebraic group, Algebraic number field, American Mathematical Society, Analytic continuation, Basic Number Theory, Class field theory, Emil Artin, Erich Hecke, Ernst Witt, Functional equation, General linear group, Harmonic analysis, Hecke character, Hervé Jacquet, International Congress of Mathematicians, Jean Dieudonné, Kenkichi Iwasawa, L-function, Langlands program, List of zeta functions, Number theory, Peter Gustav Lejeune Dirichlet, Poisson summation formula, Princeton University, Roger Godement, Thesis, Theta function, Wilfried Schmid, World War II.
1950 documents
1950 in science

Adelic algebraic group

In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A. Tate's thesis and adelic algebraic group are algebraic number theory.

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Algebraic number field

In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Tate's thesis and algebraic number field are algebraic number theory.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Analytic continuation

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function.

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Basic Number Theory

Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic methods. Tate's thesis and Basic Number Theory are algebraic number theory.

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Class field theory

In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Tate's thesis and class field theory are algebraic number theory.

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Emil Artin

Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.

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Erich Hecke

Erich Hecke (20 September 1887 – 13 February 1947) was a German mathematician known for his work in number theory and the theory of modular forms.

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Ernst Witt

Ernst Witt (26 June 1911 – 3 July 1991) was a German mathematician, one of the leading algebraists of his time.

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Functional equation

In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns.

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General linear group

In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication.

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Harmonic analysis

Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency.

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Hecke character

In number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of ''L''-functions larger than Dirichlet ''L''-functions, and a natural setting for the Dedekind zeta-functions and certain others which have functional equations analogous to that of the Riemann zeta-function. Tate's thesis and Hecke character are zeta and L-functions.

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Hervé Jacquet

Hervé Jacquet is a French American mathematician, working in automorphic forms.

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International Congress of Mathematicians

The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics.

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Jean Dieudonné

Jean Alexandre Eugène Dieudonné (1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology.

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Kenkichi Iwasawa

Kenkichi Iwasawa (岩澤健吉 Iwasawa Kenkichi, September 11, 1917 – October 26, 1998) was a Japanese mathematician who is known for his influence on algebraic number theory.

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L-function

In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. Tate's thesis and l-function are zeta and L-functions.

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Langlands program

In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and consequential conjectures about connections between number theory and geometry. Tate's thesis and Langlands program are zeta and L-functions.

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List of zeta functions

In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function Zeta functions include. Tate's thesis and List of zeta functions are zeta and L-functions.

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Number theory

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.

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Peter Gustav Lejeune Dirichlet

Johann Peter Gustav Lejeune Dirichlet (13 February 1805 – 5 May 1859) was a German mathematician.

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Poisson summation formula

In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform.

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Princeton University

Princeton University is a private Ivy League research university in Princeton, New Jersey.

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Roger Godement

Roger Godement (1 October 1921 – 21 July 2016) was a French mathematician, known for his work in functional analysis as well as his expository books.

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Thesis

A thesis (theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings.

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Theta function

In mathematics, theta functions are special functions of several complex variables.

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Wilfried Schmid

Wilfried Schmid (born May 28, 1943) is a German-American mathematician who works in Hodge theory, representation theory, and automorphic forms.

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World War II

World War II or the Second World War (1 September 1939 – 2 September 1945) was a global conflict between two alliances: the Allies and the Axis powers.

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References

[1] https://en.wikipedia.org/wiki/Tate's_thesis

Also known as Iwasawa-Tate theory, Tate thesis.