F. Tyrrell

collaborators

3 papers

math.CO2026

Multiplicative Subgroups of Prime Fields Are Not Sumsets

Misha Rudnev, Fred Tyrrell

Let $H \leq F_{p}^{*}$ be a proper multiplicative subgroup, and suppose that $H = A + B$ for some $A, B \subseteq F_{p}$ . We prove that either one of the summands is a sin…

math.CO2026

Beating Product Constructions for Linear Equations Over Finite Fields

Paul Hametner, Fred Tyrrell

We show that for any $A \subseteq F_{q}^{n}$ lacking non-trivial solutions to a translation-invariant linear equation of genus one, meaning that no nonempty proper subset of th…

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…