"Hecke L-functions"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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==introduction== | ==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 | ||
| + | * Tate's approach to analytic continuation of classical $\zeta$-functions and Dirichlet $L$-functions | ||
| + | * from '''[Leahy2010]''' | ||
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<blockquote> | <blockquote> | ||
In the early 20th century, Erich Hecke attempted to find a further generalization of the | In the early 20th century, Erich Hecke attempted to find a further generalization of the | ||
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of automorphic forms | of automorphic forms | ||
</blockquote> | </blockquote> | ||
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| + | ==Dirichlet L-functions== | ||
| + | * {{수학노트|url=디리클레_L-함수}} | ||
==related items== | ==related items== | ||
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* [[L-functions of elliptic curves with complex multiplication]] | * [[L-functions of elliptic curves with complex multiplication]] | ||
| + | * [[Adele]] | ||
==expositions== | ==expositions== | ||
| − | * James-Michael Leahy, [http://www.math.mcgill.ca/darmon/theses/leahy/thesis.pdf An introduction to Tate's Thesis] | + | * Alayont, [http://faculty.gvsu.edu/alayontf/notes/senior_thesis.pdf Adelic approach to Dirichlet L-function] |
| + | * '''[Leahy2010]''' James-Michael Leahy, [http://www.math.mcgill.ca/darmon/theses/leahy/thesis.pdf An introduction to Tate's Thesis] | ||
* Herz, Carl, Stephen William Drury, and Maruti Ram Murty. 1997. Harmonic Analysis and Number Theory: Papers in Honour of Carl S. Herz : Proceedings of a Conference on Harmonic Analysis and Number Theory, April 15-19, 1996, McGill University, Montréal, Canada. American Mathematical Soc. | * Herz, Carl, Stephen William Drury, and Maruti Ram Murty. 1997. Harmonic Analysis and Number Theory: Papers in Honour of Carl S. Herz : Proceedings of a Conference on Harmonic Analysis and Number Theory, April 15-19, 1996, McGill University, Montréal, Canada. American Mathematical Soc. | ||
2014년 7월 6일 (일) 06:17 판
introduction
- http://math.stackexchange.com/questions/409200/functional-equation-for-hecke-l-series
- Tate's approach to analytic continuation of classical $\zeta$-functions and Dirichlet $L$-functions
- from [Leahy2010]
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
Dirichlet L-functions
expositions
- Alayont, Adelic approach to Dirichlet L-function
- [Leahy2010] James-Michael Leahy, An introduction to Tate's Thesis
- Herz, Carl, Stephen William Drury, and Maruti Ram Murty. 1997. Harmonic Analysis and Number Theory: Papers in Honour of Carl S. Herz : Proceedings of a Conference on Harmonic Analysis and Number Theory, April 15-19, 1996, McGill University, Montréal, Canada. American Mathematical Soc.