A Probabilistic Approach to Generalized Skewes NumbersMPIM

by Mounir Hajani (Université Bordeaux 1/MPIM)

Wednesday Mar 25, 2026, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Number theory lunch seminar

In this talk, we study prime number races between quadratic residues and non-residues modulo $q$. Generalized Skewes numbers denote the first values for which the number of primes among quadratic residues strictly exceeds those among non-residues. I will present joint work with A. Bailleul and T. Untrau in which we disprove a conjecture of Fiorilli regarding the size of these numbers. Furthermore, assuming the Generalized Riemann Hypothesis and an effective linear independence hypothesis, we establish upper bounds for these numbers in terms of $q$.