"Hecke L-functions"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| + | ==introduction== | ||
* http://math.stackexchange.com/questions/409200/functional-equation-for-hecke-l-series | * http://math.stackexchange.com/questions/409200/functional-equation-for-hecke-l-series | ||
| + | <blockquote> | ||
| + | In the early 20th century, Erich Hecke attempted to find a further generalization of the | ||
| + | Dirichlet L-series and the Dedekind zeta function. In 1920, he introduced the notion of | ||
| + | a Grossencharakter, an ideal class character of a number field, and established the analytic | ||
| + | continuation and functional equation of its associated L-series, the Hecke L-series. In 1950, | ||
| + | John Tate, following the suggestion of his advisor, Emil Artin, recast Hecke's work. | ||
| + | Tate provided a more elegant proof of the functional equation of the Hecke L-series by using | ||
| + | Fourier analysis on the adeles and employing a reformulation of the Grossencharakter in | ||
| + | terms of a character on the ideles. Tate's work now is generally understood as the GL(1) case | ||
| + | of automorphic forms | ||
| + | </blockquote> | ||
==related items== | ==related items== | ||
| + | * {{수학노트|url=디리클레_L-함수}} | ||
* [[L-functions of elliptic curves with complex multiplication]] | * [[L-functions of elliptic curves with complex multiplication]] | ||
| + | |||
| + | |||
| + | ==expositions== | ||
| + | * James-Michael Leahy, [http://www.math.mcgill.ca/darmon/theses/leahy/thesis.pdf An introduction to Tate's Thesis] | ||
2014년 7월 6일 (일) 05:47 판
introduction
In the early 20th century, Erich Hecke attempted to find a further generalization of the Dirichlet L-series and the Dedekind zeta function. In 1920, he introduced the notion of a Grossencharakter, an ideal class character of a number field, and established the analytic continuation and functional equation of its associated L-series, the Hecke L-series. In 1950, John Tate, following the suggestion of his advisor, Emil Artin, recast Hecke's work. Tate provided a more elegant proof of the functional equation of the Hecke L-series by using Fourier analysis on the adeles and employing a reformulation of the Grossencharakter in terms of a character on the ideles. Tate's work now is generally understood as the GL(1) case of automorphic forms
expositions
- James-Michael Leahy, An introduction to Tate's Thesis