August 12, 2024Open Access

QM abelian varieties, hypergeometric character sums and modular forms

Key Points

Key points are not available for this paper at this time.

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 Tₚ acting spaces of cusp forms Sₖ () of weight k for certain arithmetically defined Fuchsian subgroups SL₂ (R). In particular we consider the groups attached to the quaternion division algebra B₆ over Q of discriminant 6.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Hoffman et al. (Mon,) studied this question.

synapsesocial.com/papers/68e5cb66b6db643587561ade https://doi.org/https://doi.org/10.48550/arxiv.2408.06562

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Traces of Hecke operators on Drinfeld modular forms for GL2(Fq[T])2026 · 1 citations
2Automatic convergence and arithmeticity of modular forms on exceptional groups2024
3ENUMERATIVE GEOMETRY: SSM CLASSES OF MULTISINGULARITIES AND CURVE COUNTING2026
4Gross's conjecture: the dihedral case2025
5Dimension formulas for modular form spaces of rational weights, the classification of eta-quotient characters and an extension of Martin's theorem2024

Bookmark

View Full Paper