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Mathematische Zeitschrift

, Volume 291, Issue 3–4, pp 1419–1434 | Cite as

Sturm bounds for Siegel modular forms of degree 2 and odd weights

  • Toshiyuki KikutaEmail author
  • Sho Takemori
Article
  • 68 Downloads

Abstract

We correct the proof of the theorem in the previous paper presented by Kikuta, which concerns Sturm bounds for Siegel modular forms of degree 2 and of even weights modulo a prime number dividing \(2\cdot 3\). We give also Sturm bounds for them of odd weights for any prime numbers, and we prove their sharpness. The results cover the case where Fourier coefficients are algebraic numbers.

Keywords

Siegel modular forms Congruences for modular forms Fourier coefficients J. Sturm 

Mathematics Subject Classification

Primary 11F33 Secondary 11F46 

Notes

Acknowledgements

The authors would like to thank the referee for a detailed reading of the manuscript, for helpful advice that improved the presentation of this paper. Toshiyuki Kikuta is supported by JSPS Kakenhi JP18K03229. Sho Takemori is partially supported by JSPS Kakenhi 23224001.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Information and Systems Engineering, Faculty of Information EngineeringFukuoka Institute of TechnologyFukuokaJapan
  2. 2.Max-Planck-Institut für MathematikBonnGermany

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