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

Dohoon Choi; YoungJu Choie; Toshiyuki Kikuta

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arXiv · 1103.0821

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

Dohoon Choi·YoungJu Choie·Toshiyuki Kikuta

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Abstract

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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BibTeX RIS

Dohoon Choi, YoungJu Choie, Toshiyuki Kikuta. 2011-03-04. Bounds for Siegel Modular Forms of genus 2 modulo $p$. https://arxiv.org/abs/1103.0821

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