Hecke operators on Hilbert-Siegel theta series
Dan Fretwell, Lynne Walling
TL;DR
This paper studies how Hecke operators act on Hilbert-Siegel theta series linked to lattices of even rank, demonstrating that average series are eigenforms and providing explicit eigenvalues.
Contribution
It introduces the action of Hecke operators on Hilbert-Siegel theta series and explicitly computes their eigenvalues, advancing understanding of their spectral properties.
Findings
Average Hilbert-Siegel theta series are eigenforms.
Eigenvalues of Hecke operators are explicitly computed.
The work enhances the understanding of automorphic forms related to lattices.
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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Mathematical Identities