Zeroes of Rankin-Selberg $L$-functions and the trace formula
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913342424088576 |
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| author | Wong, Tian An |
| author_facet | Wong, Tian An |
| contents | We express the contribution of certain maximal parabolic Eisenstein series to the spectral side of the Arthur--Selberg trace formula for GL$(n)$ in terms of zeroes of Rankin--Selberg $L$-functions, generalizing previous results for GL(2) and Hecke $L$-functions. As applications, we prove a lower bound for the sum of these zeroes, and a base change relation between the zeroes in the case $n=2$ for cyclic extensions of prime degree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02998 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zeroes of Rankin-Selberg $L$-functions and the trace formula Wong, Tian An Number Theory We express the contribution of certain maximal parabolic Eisenstein series to the spectral side of the Arthur--Selberg trace formula for GL$(n)$ in terms of zeroes of Rankin--Selberg $L$-functions, generalizing previous results for GL(2) and Hecke $L$-functions. As applications, we prove a lower bound for the sum of these zeroes, and a base change relation between the zeroes in the case $n=2$ for cyclic extensions of prime degree. |
| title | Zeroes of Rankin-Selberg $L$-functions and the trace formula |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.02998 |