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arXiv · 2408.06562

QM abelian varieties, hypergeometric character sums and modular forms

Jerome William Hoffman·Fang-Ting Tu
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Abstract

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 $S_k(\Gamma)$ of weight $k$ for certain arithmetically defined Fuchsian subgroups $\Gamma\subset \mathrm{SL}_2 (\mathbf{R})$. In particular we consider the groups attached to the quaternion division algebra $B_6$ over $\mathbf{Q}$ of discriminant 6.

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Jerome William Hoffman, Fang-Ting Tu. 2024-08-13. QM abelian varieties, hypergeometric character sums and modular forms. https://arxiv.org/abs/2408.06562

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