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On p-Adic Properties of Siegel Modular Forms

  • Siegfried BöchererEmail author
  • Shoyu Nagaoka
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (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.

Mathematics Subject Classification 2010

Primary 11F33 Secondary 11F55. 

Notes

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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.FreiburgGermany
  2. 2.Department of MathematicsKinki UniversityOsakaJapan

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