Author

F. Tyrrell

2 papers indexed here

We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.

Not the right person? Other researchers publish under this name.

Preprint Sep 2026

Sumsets of Ahlfors--David regular sets

We prove that there is an absolute constant $c>0$ such that for every finite $(\alpha,M)$-Ahlfors--David regular set $A\subseteq[N]$ with $0\leq\alpha<1$ and $M\geq2$, we have the sumset estimate \[|A+A|\geq |A|^{1+c(1-\alpha)/\log M}.\] We also prove a corresponding statement for Ahlfors--David regular sets in $[0,1]$...

F. Tyrrell · 0 citations

Preprint Jul 2026

Multiplicative Subgroups of Prime Fields Are Not Sumsets

Let $H \leq \mathbb{F}_p^*$ be a proper multiplicative subgroup, and suppose that $H = A+B$ for some $A,B \subseteq \mathbb{F}_p$. We prove that either one of the summands is a singleton, or $|A|=|B|=2$ and $|H|=4$. In particular, no proper multiplicative subgroup of $\mathbb{F}_p^*$ can be written as $A+B$ with $|A|,|...

M. Rudnev, F. Tyrrell · 4 citations · ⚡3