Skip to main content

On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups

A Correction to this article was published on 09 October 2019

This article has been updated

Abstract

We prove a formula of Petersson’s type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficients. The method in this paper is essentially a generalization of Kitaoka’s previous work which studied the full modular case, but some modification is necessary to obtain estimates which are sharp with respect to the level aspect.

This is a preview of subscription content, access via your institution.

Change history

  • 09 October 2019

    There are several inaccurate points and misprints in our article [1].

  • 09 October 2019

    There are several inaccurate points and misprints in our article [1].

References

  1. Christian, U.: Über Hilbert-Siegelsche Modulformen und Poincarésche Reihen. Math. Ann. 148, 257–307 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  2. Duke, W.: The critical order of vanishing of automorphic \(L\)-functions with large level. Invent. Math. 119, 165–174 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hua, L.K.: Introduction to Number Theory. Springer-Verlag, NY (1982)

    MATH  Google Scholar 

  4. Iwaniec, H.: Topics in classical automorphic forms, graduate studies in mathematics 17. American Mathematical Society, Providence (1997)

  5. Kamiya, Y.: Certain mean values and non-vanishing of automorphic \(L\)-functions with large level. Acta Arith. 93, 157–176 (2000)

    MATH  MathSciNet  Google Scholar 

  6. Kitaoka, Y.: Fourier coefficients of Siegel cusp forms of degree two. Nagoya Math. J. 93, 149–171 (1984)

    MATH  MathSciNet  Google Scholar 

  7. Klingen, H.: Introductory Lectures on Siegel Modular Forms, Cambridge studies in advanced mathematics 20. Cambridge University Press, London (1990)

    Book  Google Scholar 

  8. Kowalski, E., Saha, A., Tsimerman, J.: Local spectral equidistribution for Siegel modular forms and applications. Compositio Math. 148, 335–384 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kohji Matsumoto.

Additional information

Communicated by Ulf Kühn.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chida, M., Katsurada, H. & Matsumoto, K. On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups. Abh. Math. Semin. Univ. Hambg. 84, 31–47 (2014). https://doi.org/10.1007/s12188-013-0087-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12188-013-0087-x

Keywords

  • Siegel modular form
  • Fourier coefficients
  • Petersson formula

Mathematics Subject Classification

  • 11F30
  • 11F46