7 citations · 9 across the 7 of their papers we have counts for
7 papers
On the largest Sidon subset in a finite subset of
Alexandre Bailleul, Robin Riblet
We obtain a new lower bound on the largest Sidon subset of an arbitrary finite set of integers. If denotes the minimum, over all -element subsets of , of the l…
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…
Large subsets avoiding algebraic patterns
Alexandre Bailleul, Robin Riblet
We prove the existence of a subset of the torus with large sumsets and avoiding all linear patterns. This extends a result of Körner, who had shown that for any integer ,…
Exceptional biases in counting primes over functions fields
Alexandre Bailleul, Lucile Devin, Daniel Keliher +1
We study how often exceptional configurations of irreducible polynomials over finite fields occur in the context of prime number races and Chebyshev's bias. In particular, we show…
Explicit Kronecker-Weyl theorems and applications to prime number races
Alexandre Bailleul
We prove explicit versions of the Kronecker-Weyl theorems, both in a discrete and a continuous settings, without any linear independence hypothesis. As an application, we propose a…
Chebyshev's bias in dihedral and generalized quaternion Galois groups
Alexandre Bailleul
We study the inequities in the distribution of Frobenius elements in Galois extensions of the rational numbers with Galois groups that are either dihedral or (generalized)…