Samuel Mansfield

collaborators

3 papers

math.CO2025

Generalised Erdős distance theory on graphs

Sean Dewar, Nora Frankl, Samuel Mansfield +3

The famous Erdős distinct distances problem asks the following: how many distinct distances must exist between a set of $n$ points in the plane? There are many generalisations of t…

math.CO2025

Additive growth amongst images of linearly independent analytic functions

Samuel Mansfield

Let $F$ be a set of $n$ real analytic functions with linearly independent derivatives restricted to a compact interval $I$ . We show that for any finite set $A \subset I$ ,…

math.NT2023

A Quadratic Vinogradov Mean Value Theorem in Finite Fields

Samuel Mansfield, Akshat Mudgal

Let $p$ be a prime, let $s \geq 3$ be a natural number and let $A \subseteq F_{p}$ be a non-empty set satisfying $∣ A ∣ ≪ p^{1/2}$ . Denoting $J_{s} (A)$ to be the number of sol…