QM abelian varieties, hypergeometric character sums and modular forms

Fuente: arXiv
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Main Authors: Hoffman, Jerome William, Tu, Fang-Ting
Format: Preprint
Published: 2024
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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
id 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