Péa Bazin

collaborators

2 papers

math.NT2026

Bounded Exponential Sums with Multiplicative Coefficients

Pierre-Alexandre Bazin, Ihor Pylaiev, Fred Tyrrell

We investigate when the exponential sum $S_{f} (x, I^\pm) := \sum_{n \leq x} f (n) e (n I^\pm)$ is bounded, for a multiplicative function $f$ and $I^\pm \in R$ . We show that under natu…

math.NT2025

Exponential sums over primes are unbounded

Pierre-Alexandre Bazin, Péa Bazin

We prove prime exponential sums have no better than square root cancellation on average on short intervals, in the sense that $$\frac{1}{x} \sum_{-y< n\le x} \left|\sum_{\substack{…