Sophie Stevens

activity

20162021

most citedAn Improved Point-Line Incidence Bound Over Arbitrary Fields

55 citations · 99 across the 6 of their papers we have counts for

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Showing 2021Show all

3 papers · 1 filter

math.CO2021

Attaining the exponent $5/4$ for the sum-product problem in finite fields

Ali Mohammadi, Sophie Stevens

We improve the exponent in the finite field sum-product problem from $11/9$ to $5/4$ , improving the results of Rudnev, Shakan and Shkredov. That is, we show that if $A\subset \math…

math.CO2021★ 7 cited

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 $A, B \subseteq R$ finite sets, and for all $f, g$ convex or co…

math.CO2021★ 1 cited

Low-energy decomposition results over finite fields

Ali Mohammadi, Sophie Stevens

We prove various low-energy decomposition results, showing that we can decompose a finite set $A \subset F_{p}$ satisfying $∣ A ∣ < p^{5/8}$ , into $A = S ⊔ T$ so that, for a…

Attaining the exponent 5/4 for the sum-product problem in finite fields

On sum sets of convex functions

Low-energy decomposition results over finite fields

Attaining the exponent $5/4$ for the sum-product problem in finite fields