Prolongement analytique de fonctions $\zeta$ et de fonctions $L$

Pierre Colmez

Prolongement analytique de fonctions $\zeta$ et de fonctions $L$

Number Theory 2024-05-14 v2 History and Overview Representation Theory

Authors: Pierre Colmez

Abstract

Wiles' work on Fermat's last Theorem highlighted the power of $p$ -adic methods to prove the existence of analytic continuations of $\zeta$ and $L$ functions. These methods have become considerably more sophisticated in recent years, and have produced a wealth of beautiful results: Hasse--Weil conjecture for genus $2$ curves, holomorphy of $L$ -functions of symmetric powers of modular forms, etc. We present some of these advances.

Keywords

analytic continuation zeta function l-function p-adic methods hasse-weil conjecture modular forms

Cite

@article{arxiv.2311.15905,
  title  = {Prolongement analytique de fonctions $\zeta$ et de fonctions $L$},
  author = {Pierre Colmez},
  journal= {arXiv preprint arXiv:2311.15905},
  year   = {2024}
}

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Bourbaki talk november 2023, in French language, final version

Prolongement analytique de fonctions $\zeta$ et de fonctions $L$

Abstract

Keywords

Cite

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