Prolongement analytique de fonctions $ζ$ et de fonctions $L$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911873478164480 |
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| author | Colmez, Pierre |
| author_facet | Colmez, Pierre |
| contents | Wiles' work on Fermat's last Theorem highlighted the power of $p$-adic methods to prove the existence of analytic continuations of $ζ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15905 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Prolongement analytique de fonctions $ζ$ et de fonctions $L$ Colmez, Pierre Number Theory History and Overview Representation Theory 11Fxx Wiles' work on Fermat's last Theorem highlighted the power of $p$-adic methods to prove the existence of analytic continuations of $ζ$ 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. |
| title | Prolongement analytique de fonctions $ζ$ et de fonctions $L$ |
| topic | Number Theory History and Overview Representation Theory 11Fxx |
| url | https://arxiv.org/abs/2311.15905 |