4 papers · 1 filter
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…
Wasserstein metrics and quantitative equidistribution of exponential sums over finite fields
Emmanuel Kowalski, Théo Untrau
The Wasserstein distance between probability measures on compact spaces provides a natural invariant quantitative measure of equidistribution, which is partly similar to the classi…
Ultra-short sums of trace functions
Emmanuel Kowalski, Théo Untrau
We generalize results of Duke, Garcia, Hyde, Lutz and others on the distribution of sums of roots of unity related to Gaussian periods to obtain equidistribution of similar sums ov…
Equidistribution of exponential sums indexed by a subgroup of fixed cardinality
Théo Untrau
We consider families of exponential sums indexed by a subgroup of invertible classes modulo some prime power . For fixed , we restrict to moduli so that there is a unique…