La fonction Zeta de Riemann prend une infinite de valeurs irrationnelles aux entiers impairs

Abstract

We provide a lower bound for the dimension of the vector space spanned by 1 and by the values of the Riemann Zeta function at the first odd integers. As a consequence, the Zeta function takes infinitely many irrational values at odd integers.

4 pages (french), accepted for publication (Comptes rendus de l'Academie des sciences de Paris)

Cited by in corpus (16)

• Quantum Correlations and Number Theory
• Generalized Lambert series and arithmetic nature of odd zeta values
• Many odd zeta values are irrational
• An Euler-type formula for $\beta (2n)$ and closed-form expressions for a class of zeta series
• Asymptotic relations for weighted finite multiple zeta values
• A note on the number of irrational odd zeta values
• A Linear independence result for $p$-adic $L$-values
• Well-poised generation of Apéry-like recursions
• Odd zeta motive and linear forms in odd zeta values
• Irrationality of values of L-functions of Dirichlet characters
• Evaluation of Log-tangent Integrals by series involving $\zeta (2n+1)$
• Hypergeometric rational approximations to $\zeta (4)$
• Supersymmetric zeta functions and determinants
• Manifest Modular Invariance in the Near-Critical Ising Model
• A Number Field Analogue of Ramanujan's identity for $\zeta (2m+1)$
• A note on the irrationality of ${\zeta }_2(5)$