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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2003.03450 |
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| _version_ | 1866911674508771328 |
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| author | Yang, Liyang |
| author_facet | Yang, Liyang |
| contents | In this paper we establish a coarse Jacquet-Zagier trace identity for GL$(n).$ We prove the absolute convergence when $\Re(s)>1$ and $0<\Re(s)<1;$ and obtain holomorphic continuation under almost all character twist. Moreover, as an application, we prove that holomorphy of certain adjoint $L$-functions for GL$(n)$ implies Dedekind conjecture of degree $n$. Some nonvanishing results are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_03450 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Coarse Jacquet-Zagier Trace Formula for GL($n$) with Applications Yang, Liyang Number Theory In this paper we establish a coarse Jacquet-Zagier trace identity for GL$(n).$ We prove the absolute convergence when $\Re(s)>1$ and $0<\Re(s)<1;$ and obtain holomorphic continuation under almost all character twist. Moreover, as an application, we prove that holomorphy of certain adjoint $L$-functions for GL$(n)$ implies Dedekind conjecture of degree $n$. Some nonvanishing results are also discussed. |
| title | A Coarse Jacquet-Zagier Trace Formula for GL($n$) with Applications |
| topic | Number Theory |
| url | https://arxiv.org/abs/2003.03450 |