3 papers
math.NT2026
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…
math.NT2025
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…
math.NT2023
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…