Brandon Hanson

activity

20122023

most citedRefined Estimates Concerning Sumsets Contained in the Roots of Unity

30 citations · 59 across the 14 of their papers we have counts for

collaborators

18 papers

math.NT2023★ 1 cited

The sum-product problem for integers with few prime factors

Brandon Hanson, Misha Rudnev, Ilya Shkredov +1

It was asked by E. Szemerédi if, for a finite set $A \subset Z$ , one can improve estimates for $max {∣ A + A ∣, ∣ A \cdot A ∣}$ , under the constraint that all integers involved ha…

math.CO2021★ 1 cited

Convexity, Superquadratic Growth, and Dot Products

Brandon Hanson, Oliver Roche-Newton, Steven Senger

Let $P \subset R^{2}$ be a point set with cardinality $N$ . We give an improved bound for the number of dot products determined by $P$ , proving that, \[ |\{ p \cdot q :p,q \in…

math.NT2021

Higher Convexity and Iterated Second Moment Estimates

Peter J. Bradshaw, Brandon Hanson, Misha Rudnev

We prove bounds for the number of solutions to $a_{1} + \dots + a_{k} = a_{1}^{'} + \dots + a_{k}^{'}$ over $N$ -element sets of reals, which are sufficiently convex or near-convex. A near-conv…

math.CO2020

A question of Bukh on sums of dilates

Brandon Hanson, Giorgis Petridis

We answer in the affirmative a question of Bukh on the cardinality of the dilate sum $A + 2 \cdot A$ .

math.NT2020

Higher convexity and iterated sum sets

Brandon Hanson, Oliver Roche-Newton, Misha Rudnev

Let $f$ be a smooth real function with strictly monotone first $k$ derivatives. We show that for a finite set $A$ , with $∣ A + A ∣ \leq K ∣ A ∣$ , $|2^kf(A)-(2^k-1)f(A)|\gg_k |A|^{k+1-o(1)}…

math.NT2020

Littlewood's problem for sets with multidimensional structure

Brandon Hanson

We give $L^{1}$ -norm estimates for exponential sums of a finite sets $A$ consisting of integers or lattice points. Under the assumption that $A$ possesses sufficient multidimensional…