Sturm bounds for Siegel modular forms of degree 2 and odd weights
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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.
KeywordsSiegel modular forms Congruences for modular forms Fourier coefficients J. Sturm
Mathematics Subject ClassificationPrimary 11F33 Secondary 11F46
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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