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Modular forms in Pari/GP

  • Karim Belabas
  • Henri CohenEmail author
Research
  • 87 Downloads
Part of the following topical collections:
  1. Modular Forms are Everywhere: Celebration of Don Zagier’s 65th Birthday

Abstract

We give theoretical and practical information on the Pari/GP modular forms package available since the spring of 2018. Thanks to the use of products of two Eisenstein series, this package is the first which can compute Fourier expansions at any cusps, evaluate modular forms near the real axis, evaluate L-functions of noneigenforms, and compute general Petersson scalar products.

Notes

Acknowledgements

We would like to thank B. Allombert, J. Bober, A. Booker, M. Lee, and B. Perrin-Riou for very helpful discussions and help in algorithms and programming, F. Brunault and M. Neururer for Theorem 7, as well as K. Khuri-Makdisi, N. Mascot, N. Billerey and E. Royer. Last but not least, we thank Don Zagier for his continuous input on this package and on Pari/GP in general. In addition, note that a much smaller program written 30 years ago by Don, N. Skoruppa, and the second author can be considered as an ancestor to the present package.

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Copyright information

© SpringerNature 2018

Authors and Affiliations

  1. 1.CNRS, INRIA, IMB, UMR 5251Univ. BordeauxTalenceFrance

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