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Book Sections Year : 2019

Expansions at Cusps and Petersson Products in Pari/GP

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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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Dates and versions

hal-01883070 , version 1 (27-09-2018)

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Henri Cohen. Expansions at Cusps and Petersson Products in Pari/GP. Johannes Blümlein; Carsten Schneider; Peter Paule. Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Springer, 2019, Texts & Monographs in Symbolic Computation. ⟨hal-01883070⟩
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