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Expansions at Cusps and Petersson Products in Pari/GP

Henri Cohen 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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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Submitted on : Thursday, September 27, 2018 - 4:16:54 PM
Last modification on : Saturday, December 4, 2021 - 3:43:33 AM
Long-term archiving on: : Friday, December 28, 2018 - 5:34:14 PM


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  • HAL Id : hal-01883070, version 1
  • ARXIV : 1809.10908



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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