Hecke operators on Hilbert-Siegel theta series

2019/09/04 by Dan Fretwell, Fretwell, Dan, Lynne H. Walling +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1909.01852

openalex publication_date 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the action of Hecke-type operators on Hilbert-Siegel theta series attached to lattices of even rank. We show that average Hilbert-Siegel theta series are eigenforms for these operators, and we explicitly compute the eigenvalues.

Related

• Action of Hecke operators on Siegel theta series II
• Hecke actions on certain strongly modular genera of lattices
• A formula for the action of Hecke operators on half-integral weight Siegel modular forms and applications
• Hecke eigenvalues and relations for degree 2 Siegel Eisenstein series
• A Siegel cusp form of degree 12 and weight 12