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Expansions at Cusps and Petersson Products in Pari/GP

  • Henri CohenEmail author
Chapter
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)

Abstract

We begin by explaining how to compute Fourier expansions at all cusps of any modular form of integral or half-integral weight thanks to a theorem of Borisov–Gunnells and explicit expansions of Eisenstein series at all cusps. Using this, we then give a number of methods for computing arbitrary Petersson products. All this is available in the current release of the Pari/GP package.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut de Mathématiques de Bordeaux (IMB)Université de Bordeaux, UMR 5251 du CNRS, Equipe LFANT INRIATalence CedexFrance

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