Péa Bazin

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math.NT2025

Exponential sums over primes are unbounded

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{…

math.NT2025

Bounded Exponential Sums with Multiplicative Coefficients

Pierre-Alexandre Bazin, Ihor Pylaiev, Fred Tyrrell

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