On $p$-divisibility of Fourier coefficients of Siegel modular forms

TL;DR

This paper investigates the p-divisibility properties of Fourier coefficients of Siegel modular forms, extending known results and providing new insights into their divisibility behavior.

Contribution

It introduces a p-divisibility transposition framework for Fourier coefficients of Siegel modular forms, supplementing existing results like Wilton's on the Ramanujan tau-function.

Findings

Describes p-divisibility transposition for Fourier coefficients

Extends Wilton's results to Siegel modular forms

Provides new divisibility criteria for Fourier coefficients

Abstract

We describe the $p$-divisibility transposition for the Fourier coefficients of Siegel modular forms. This provides a supplement to the result by Wilton for $p$-divisibility satisfied by the Ramanujan $\tau$-function.