Brandon Hanson

activity

20122021

collaborators

7 papers

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.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…

math.NT2019

Refined Estimates Concerning Sumsets Contained in the Roots of Unity

Brandon Hanson, Giorgis Petridis

We prove that the clique number of the Paley graph is at most $p /2 + 1$ , and that any supposed additive decompositions of the set of quadratic residues can only come from co…

math.CO2019

Long regularly-spaced and convex sequences in dense sets of integers

Brandon Hanson

Let A be a set of integers dense in a finite interval. We establish upper and lower bounds for the longest regularly-spaced and convex subsets of A and of A-A.

math.NT2018

On iterated product sets with shifts II

Brandon Hanson, Oliver Roche-Newton, Dmitrii Zhelezov

The main result of this paper is the following: for all $b \in Z$ there exists $k = k (b)$ such that \[ \max \{ |A^{(k)}|, |(A+u)^{(k)}| \} \geq |A|^b, \] for any finite $A \s…