Computational Number Theory in Relation with L-Functions

Henri Cohen 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums), and in the global case (for instance Dirichlet L-functions, involving in particular the study of inverse Mellin transforms); we also give a number of little-known but very useful numerical methods, usually but not always related to the computation of L-functions.
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Henri Cohen. Computational Number Theory in Relation with L-Functions. Ilker Inam; Engin Büyükaşık. Notes from the International School on Computational Number Theory, Birkhäuser, pp.171-266, 2019, Tutorials, Schools, and Workshops in the Mathematical Sciences, ⟨10.1007/978-3-030-12558-5_3⟩. ⟨hal-01883052⟩

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