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On Siegel modular forms of level p and their properties mod p

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Abstract

Using theta series we construct Siegel modular forms of level p which behave well modulo p in all cusps. This construction allows us to show (under a mild condition) that all Siegel modular forms of level p and weight 2 are congruent mod p to level one modular forms of weight p + 1; in particular, this is true for Yoshida lifts of level p.

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Authors and Affiliations

  1. Kunzenhof 4B, Freiburg, 79117, Germany

    Siegfried Böcherer

  2. Department of Mathematics, Kinki University, Higashi-Osaka, Japan

    Shoyu Nagaoka

Authors
  1. Siegfried Böcherer
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  2. Shoyu Nagaoka
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Correspondence to Shoyu Nagaoka.

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Böcherer, S., Nagaoka, S. On Siegel modular forms of level p and their properties mod p . manuscripta math. 132, 501–515 (2010). https://doi.org/10.1007/s00229-010-0357-1

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  • DOI: https://doi.org/10.1007/s00229-010-0357-1

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