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Computing L-Functions of Quadratic Characters at Negative Integers

Henri Cohen 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We survey a number of different methods for computing $L(\chi,1-k)$ for a Dirichlet character $\chi$, with particular emphasis on quadratic characters. The main conclusion is that when $k$ is not too large (for instance $k\le100$) the best method comes from the use of Eisenstein series of half-integral weight, while when $k$ is large the best method is the use of the complete functional equation, unless the conductor of $\chi$ is really large, in which case the previous method again prevails.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03139244
Contributor : Andreas Enge Connect in order to contact the contributor
Submitted on : Thursday, February 11, 2021 - 6:11:48 PM
Last modification on : Saturday, December 4, 2021 - 3:44:01 AM

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  • HAL Id : hal-03139244, version 1
  • ARXIV : 2101.10432

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Henri Cohen. Computing L-Functions of Quadratic Characters at Negative Integers. 2021. ⟨hal-03139244⟩

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