5 papers
On the role of higher roots in prime ideal races
Mounir Hayani
Let be a Galois extension of number fields, and let be conjugacy classes of . By introducing algebraic parameters related to and , we…
Chebyshev's bias without linear independence
Mounir Hayani
We confirm Chebyshev's observation that primes are strikingly more abundant in non-square residue classes modulo a fixed integer under the Generalized Riemann Hypothesis (GRH) by p…
A Wasserstein metric approach to generalized Skewes' numbers. I. Prime number races
Alexandre Bailleul, Mounir Hayani, Théo Untrau
We study generalized Skewes' numbers, which are the locations of the first sign change between two comparable prime counting functions. In the context of the race between quadratic…
Prime Ideal Races With Several Competitors
A Bailleul, M Hayani
We investigate races among prime ideals in number fields when there are two or more competing conjugacy classes. In their work [4], Fiorilli and Jouve studied two-way races in numb…
Disproving a weaker form of Hooley's conjecture
Mounir Hayani
Hooley conjectured that , as soon as , where represents the variance of primes in arithmetic progressions modulo , weighted…