Cédric Pilatte

collaborators

3 papers

math.NT2026

Improved bounds for the Fourier uniformity conjecture

CÃ©dric Pilatte

Let $I^»$ denote the Liouville function. We prove that $X \leq x < 2 X \sum I^\pm \in R / Z sup x \leq n < x + H \sum I^» (n) e (n I^\pm) = o (H X)$ …

math.NT2025

Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms

CÃ©dric Pilatte

In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of…

math.NT2025

Improved bounds for the two-point logarithmic Chowla conjecture

Let $I^»$ be the Liouville function, defined as $I^» (n) := (- 1)^{I^c ◯ (n)}$ where $I^c ◯ (n)$ is the number of prime factors of $n$ with multiplicity. In 2021, Helfgott and RadziwiÅÅ prov…