Sur un crit\`ere de Baez-Duarte pour l'hypoth\`ese de Riemann

TL;DR

This paper explores a Hilbert space criterion related to the Riemann hypothesis, improving existing estimates under the assumption that the hypothesis is true, thus contributing to the analytical understanding of this famous conjecture.

Contribution

It refines the estimate for a Hilbert space distance criterion for the Riemann hypothesis based on Baez-Duarte's reformulation, assuming the hypothesis holds.

Findings

Improved estimate for the Hilbert space distance under RH

Strengthened connection between fractional parts and RH

Provides analytical bounds assuming RH

Abstract

Baez-Duarte reformulated the Riemann hypothesis as a statement about a Hilbert space distance, involving the integer dilations of the "fractional part" function. Under the assumption of the Riemann hypothesis, we improve on the currently known estimate for this distance.