Non-vanishing of certain integral representations
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912304873865216 |
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| author | Yadav, Akash |
| author_facet | Yadav, Akash |
| contents | In this paper, we prove that there exist Whittaker and Schwartz functions such that the local Flicker integrals are non-vanishing for all complex values of $s$, and the local Bump-Friedberg integrals are non-vanishing for all complex pairs $(s_1,s_2)$. As a corollary, we determine the potential locations of poles for their corresponding partial $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-vanishing of certain integral representations Yadav, Akash Number Theory Representation Theory 11F70, 22E55 In this paper, we prove that there exist Whittaker and Schwartz functions such that the local Flicker integrals are non-vanishing for all complex values of $s$, and the local Bump-Friedberg integrals are non-vanishing for all complex pairs $(s_1,s_2)$. As a corollary, we determine the potential locations of poles for their corresponding partial $L$-functions. |
| title | Non-vanishing of certain integral representations |
| topic | Number Theory Representation Theory 11F70, 22E55 |
| url | https://arxiv.org/abs/2412.10534 |