QM abelian varieties, hypergeometric character sums and modular forms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911986318573568 |
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| author | Hoffman, Jerome William Tu, Fang-Ting |
| author_facet | Hoffman, Jerome William Tu, Fang-Ting |
| contents | This is a report on recent work, with Wen-Ching Winnie Li and Ling Long. In that work explicit formulas are given, involving hypergeometric character sums, for the traces of Hecke operators $T_p$ acting spaces of cusp forms $S_k(Γ)$ of weight $k$ for certain arithmetically defined Fuchsian subgroups $Γ\subset \mathrm{SL}_2 (\mathbf{R})$. In particular we consider the groups attached to the quaternion division algebra $B_6$ over $\mathbf{Q}$ of discriminant 6. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_06562 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | QM abelian varieties, hypergeometric character sums and modular forms Hoffman, Jerome William Tu, Fang-Ting Number Theory 11T23, 11T24, 11S40, 11F80, 11F85, 33C05, 33C65 This is a report on recent work, with Wen-Ching Winnie Li and Ling Long. In that work explicit formulas are given, involving hypergeometric character sums, for the traces of Hecke operators $T_p$ acting spaces of cusp forms $S_k(Γ)$ of weight $k$ for certain arithmetically defined Fuchsian subgroups $Γ\subset \mathrm{SL}_2 (\mathbf{R})$. In particular we consider the groups attached to the quaternion division algebra $B_6$ over $\mathbf{Q}$ of discriminant 6. |
| title | QM abelian varieties, hypergeometric character sums and modular forms |
| topic | Number Theory 11T23, 11T24, 11S40, 11F80, 11F85, 33C05, 33C65 |
| url | https://arxiv.org/abs/2408.06562 |