Bounds for Siegel Modular Forms of genus 2 modulo $p$

Details Bounds for Siegel Modular Forms of genus 2 modulo $p$ Bounds for Siegel Modular Forms of genus 2 modulo $p$

2011-03-04

arxiv.org/abs/1103.0821v1

Mathematics

Number Theory

Scientific paper

Sturm obtained the bounds for the number of the first Fourier coefficients of elliptic modular form $f$ to determine vanishing of $f$ modulo a prime $p$. In this paper, we study analogues of Sturm's bound for Siegel modular forms of genus 2. We show the resulting bound is sharp. As an application, we study congruences involving Atkin's $U(p)$-operator for the Fourier coefficients of Siegel mdoular forms of genus 2.

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