La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs

2000/08/01 by Tanguy Rivoal · 3 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Constant (computer programming) #Dimension (graph theory) #Irrational number #Meromorphic and Entire Functions #Number theory #Rational number #Riemann hypothesis #Riemann zeta function #math.NT #msc:11J72

paper · pdf · doi:10.1016/s0764-4442(00)01624-4

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

openalex publication_date 2000/08/01 · arxiv created 2000/08/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Cited by

• The Classical Theory of Zeta and L-Functions
• Asymptotic relations for truncated multiple zeta values
• Apéry's constant [wikipedia]