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Sturm type theorem for Siegel modular forms of genus 2 modulo $p$

Volume 158 / 2013

Dohoon Choi, YoungJu Choie, Toshiyuki Kikuta Acta Arithmetica 158 (2013), 129-139 MSC: 11F46, 11F33. DOI: 10.4064/aa158-2-2

Abstract

Suppose that $f$ is an elliptic modular form with integral coefficients. Sturm obtained bounds for a nonnegative integer $n$ such that every Fourier coefficient of $f$ vanishes modulo a prime $p$ if the first $n$ Fourier coefficients of $f$ are zero modulo $p$. In the present note, we study analogues of Sturm's bounds for Siegel modular forms of genus 2. As an application, we study congruences involving an analogue of Atkin's $U(p)$-operator for the Fourier coefficients of Siegel modular forms of genus 2.

Authors

  • Dohoon ChoiSchool of Liberal Arts and Sciences
    Korea Aerospace University
    200-1, Hwajeon-dong
    Goyang, Gyeonggi 412-791, Korea
    e-mail
  • YoungJu ChoieDepartment of Mathematics
    Pohang University of Science and Technology
    Pohang, 790-784, Korea
    e-mail
  • Toshiyuki KikutaDepartment of Mathematics
    Interdisciplinary Graduate School of Science and Engineering
    Kinki University
    Higashi-Osaka, 577-8502, Japan
    e-mail

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