"Marvelous cancellations": T.J. Stieltjes' letters concerning the zeta function

TL;DR

This paper presents translated letters from T.J. Stieltjes to C. Hermite discussing his claims about solving Riemann's conjecture, highlighting historical mathematical debates on the zeros of the zeta function.

Contribution

It provides new translations and insights into Stieltjes' correspondence, shedding light on his efforts and beliefs regarding the Riemann hypothesis.

Findings

Stieltjes believed all roots of the zeta function are real.

His published notes claimed to have solved Riemann's conjecture.

The letters reveal his reasoning and correspondence with Hermite.

Abstract

This article introduces and translates letters from T.J. stieltjes (1856-1894) to C. Hermite (1822-1891) regarding Stieltjes' published notes claiming to have solved B. Riemann's conjecture "it is very probable that all the roots [of the zeta function] are real."