PhD students

It is well known about the Riemann zeta function that $\zeta(2i) \in \mathbb{Q}\pi^{2i}, i\geqslant 1$, and thus all these numbers are linearly independent over $\mathbb{Q}$, since $\pi$ is transcendental.
However, very little is known about the numbers $\zeta(2i+1), i\geqslant 1$. It was proved in 1978 that $\zeta(3)$ is irrational, and in 2000 that infinitely many of these numbers are irationnal.

The aim of this talk is to introduce the core ideas used to prove such a result, and to elaborate on the new ideas that allowed many generalizations since the 2000s (better bound on the proportion of irrational numbers, broader class of functions rather than just $\zeta$, …)

TBA

TBA

TBA