7 citations · 7 across the 2 of their papers we have counts for
11 papers
Incidences of Cubic Curves in Finite Fields
Audie Warren
In this paper we prove an incidence bound for points and cubic curves over prime fields. The methods generalise those used by Mohammadi, Pham, and Warren (2021).
Additive and multiplicative Sidon sets
Oliver Roche-Newton, Audie Warren
We give a construction of a set such that any subset with is neither an additive nor multiplicative Sidon set. In doing so…
On sum sets of convex functions
Sophie Stevens, Audie Warren
In this paper we prove new bounds for sums of convex or concave functions. Specifically, we prove that for all finite sets, and for all convex or co…
The Elekes-Szabó Problem and the Uniformity Conjecture
Mehdi Makhul, Oliver Roche-Newton, Sophie Stevens +1
In this paper we give a conditional improvement to the Elekes-Szabó problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}…
The Spherical Kakeya Problem in Finite Fields
Mehdi Makhul, Audie Warren, Arne Winterhof
We study subsets of the -dimensional vector space over the finite field , for odd , which contain either a sphere for each radius or a sphere for each first coo…
Arcs in
Oliver Roche-Newton, Audie Warren
An arc is a subset of which does not contain any collinear triples. Let denote the number of arcs in with cardinality . This paper is pr…