F. Tyrrell

activity

20222026

collaborators

5 papers

math.CO2026

Sumsets of Ahlfors--David regular sets

Fred Tyrrell

We prove that there is an absolute constant $c > 0$ such that for every finite $(α, M)$ -Ahlfors--David regular set $A \subseteq [N]$ with $0 \leq α < 1$ and $M \geq 2$ , we have the sumset est…

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.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…

math.CO2022

New Lower Bounds for Cap Sets

Fred Tyrrell

A cap set is a subset of $F_{3}^{n}$ with no solutions to $x + y + z = 0$ other than when $x = y = z$ . In this paper, we provide a new lower bound on the size of a maximal cap set. Buil…