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

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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.

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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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Authors and Affiliations

  1. Department of Information and Systems Engineering, Faculty of Information Engineering, Fukuoka Institute of Technology, 3-30-1 Wajiro-higashi, Higashi-ku, Fukuoka, 811-0295, Japan

    Toshiyuki Kikuta

  2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Sho Takemori

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  1. Toshiyuki Kikuta
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  2. Sho Takemori
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Correspondence to Toshiyuki Kikuta.

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Kikuta, T., Takemori, S. Sturm bounds for Siegel modular forms of degree 2 and odd weights. Math. Z. 291, 1419–1434 (2019). https://doi.org/10.1007/s00209-018-2213-z

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  • DOI: https://doi.org/10.1007/s00209-018-2213-z

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