JOHANSSON, Fredrik

Metadatos

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Licencia de uso del documento

JOHANSSON, Fredrik
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]

Idioma

Document de travail - Pré-publication

Resumen en inglés

We consider computing the Riemann zeta function $\zeta(s)$ and Dirichlet $L$-functions $L(s,\chi)$ to $p$-bit accuracy for large $p$. Using the approximate functional equation together with asymptotically fast computation of the incomplete gamma function, we observe that $p^{3/2+o(1)}$ bit complexity can be achieved if $s$ is an algebraic number of fixed degree and with algebraic height bounded by $O(p)$. This is an improvement over the $p^{2+o(1)}$ complexity of previously published algorithms and yields, among other things, $p^{3/2+o(1)}$ complexity algorithms for Stieltjes constants and $n^{3/2+o(1)}$ complexity algorithms for computing the $n$th Bernoulli number or the $n$th Euler number exactly.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191431

Proyecto ANR

Sûreté numérique pour les preuves assistées par ordinateur - ANR-20-CE48-0014

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251