Weighted low-lying zeros of L-functions attached to Siegel modular forms
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908306278187008 |
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| author | Zhao, Shifan |
| author_facet | Zhao, Shifan |
| contents | In this paper, we study weighted low-lying zeros of spinor and standard $L$-functions attached to degree 2 Siegel modular forms. We show the symmetry type of weighted low-lying zeros of spinor $L$-functions is symplectic, for test functions whose Fourier transform have support in $(-1,1)$, extending the previous range $(-\frac{4}{15},\frac{4}{15})$ by E. Kowalski, A. Saha and J. Tsimerman . We then show the symmetry type of weighted low-lying zeros of standard $L$-functions is also symplectic. We further extend the range of support by performing an average over weight. As an application, we discuss non-vanishing of central values of those $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted low-lying zeros of L-functions attached to Siegel modular forms Zhao, Shifan Number Theory Primary 11F46, 11F66, 11F72 In this paper, we study weighted low-lying zeros of spinor and standard $L$-functions attached to degree 2 Siegel modular forms. We show the symmetry type of weighted low-lying zeros of spinor $L$-functions is symplectic, for test functions whose Fourier transform have support in $(-1,1)$, extending the previous range $(-\frac{4}{15},\frac{4}{15})$ by E. Kowalski, A. Saha and J. Tsimerman . We then show the symmetry type of weighted low-lying zeros of standard $L$-functions is also symplectic. We further extend the range of support by performing an average over weight. As an application, we discuss non-vanishing of central values of those $L$-functions. |
| title | Weighted low-lying zeros of L-functions attached to Siegel modular forms |
| topic | Number Theory Primary 11F46, 11F66, 11F72 |
| url | https://arxiv.org/abs/2403.19687 |