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Article Dans Une Revue Mathematics of Computation Année : 2021

FAST MULTI-PRECISION COMPUTATION OF SOME EULER PRODUCTS

Guillaume Bertoli
  • Fonction : Auteur
Gilles Vilmart

Résumé

For every modulus q ≥ 3, we define a family of subsets A of the multiplicative group (Z/qZ) × for which the Euler product p+qZ∈A (1 − p −s) can be computed with high numerical precision, where s > 1 is some given real number. We provide a Sage script to do so, and extend our result to compute Euler products p+qZ∈A F (1/p s)/H(1/p s) where F and H are polynomials with real coefficients, when this product converges absolutely. This enables us to give precise values of several Euler products occurring in number theory.
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Dates et versions

hal-03381427 , version 1 (16-10-2021)

Identifiants

Citer

Guillaume Bertoli, Christophe Besse, Gilles Vilmart. FAST MULTI-PRECISION COMPUTATION OF SOME EULER PRODUCTS. Mathematics of Computation, 2021, 90 (331), pp.2247-2265. ⟨10.1090/mcom/3630⟩. ⟨hal-03381427⟩
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