Theta operators on Siegel modular forms and Galois representations
Alexandru Ghitza, Angus McAndrew
TL;DR
This paper investigates how certain differential operators influence the Galois representations associated with Siegel modular eigenforms, aiming to deepen understanding of their interplay in number theory.
Contribution
It provides a detailed analysis of the impact of specific theta operators on Galois representations linked to Siegel modular forms, connecting differential operators with Galois theory.
Findings
Describes the effect of theta operators on Galois representations
Links differential operators to properties of Siegel modular forms
Contributes to understanding the conjectural relationship between modular forms and Galois representations
Abstract
We describe the effect of the differential operators defined by Boecherer-Nagaoka, Flander-Ghitza and Yamauchi on the Galois representations (conjecturally) attached to Siegel modular eigenforms.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models