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Automorphic Forms pp 47–66Cite as

On p-Adic Properties of Siegel Modular Forms

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 115))

Abstract

We show that Siegel modular forms of level \(\Gamma _{0}(p^{m})\) are p-adic modular forms. Moreover we show that derivatives of such Siegel modular forms are p-adic. Parts of our results are also valid for vector-valued modular forms. In our approach to p-adic Siegel modular forms we follow Serre [18] closely; his proofs however do not generalize to the Siegel case or need some modifications.

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Acknowledgements

Crucial work on this paper was done during our stay at the Mathematisches Forschungsinstitut Oberwolfach under the programme “Research in Pairs”; we continued our work during research visits at Kinki University and Universität Mannheim (respectively); a final revision was done, when the first author held a guest professorship at the University of Tokyo. We thank these institutions for the support. We also thank Dr.Kikuta for pointing out some gaps in our presentation and Professor T.Ichikawa for discussions about p-adic modular forms.

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Authors and Affiliations

  1. Kunzenhof 4B, Freiburg, 79117, Germany

    Siegfried Böcherer

  2. Department of Mathematics, Kinki University, 577-8502, Osaka, Japan

    Shoyu Nagaoka

Authors
  1. Siegfried Böcherer
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  2. Shoyu Nagaoka
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Corresponding author

Correspondence to Siegfried Böcherer .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Science, German University of Technology in Oman, Muscat, Oman

    Bernhard Heim

  2. Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman

    Mehiddin Al-Baali

  3. Department of Mathematics Graduate School of Science, Osaka University, Osaka, Japan

    Tomoyoshi Ibukiyama

  4. Department of Mathematics and Science, German University of Technology in Oman, Muscat, Oman

    Florian Rupp

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Böcherer, S., Nagaoka, S. (2014). On p-Adic Properties of Siegel Modular Forms. In: Heim, B., Al-Baali, M., Ibukiyama, T., Rupp, F. (eds) Automorphic Forms. Springer Proceedings in Mathematics & Statistics, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-319-11352-4_4

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