12 citations · 57 across the 19 of their papers we have counts for
4 papers · 1 filter
Fourier analysis and expanding phenomena in finite fields
Derrick Hart, Liangpan Li, Chun-Yen Shen
In this paper the authors study set expansion in finite fields. Fourier analytic proofs are given for several results recently obtained by Solymosi, Vinh and Vu using spectral grap…
Sum-product inequalities with perturbation
Spencer Backman, Ernie Croot, Derrick Hart +1
Suppose that A is a set of n real numbers, each at least 1 apart. Define the ``perturbed sum and product sets'' S and P to be the sums a + b + f(a,b) and products (a+g(a,b))(b+h(a,…
k-fold sums from a set with few products
Ernie Croot, Derrick Hart
In the present paper we show that if A is a set of n real numbers, and the product set A.A has at most n^(1+c) elements, then the k-fold sumset kA has at least n^(log(k/2)/2 log 2…
Pinned distance sets, k-simplices, Wolff's exponent in finite fields and sum-product estimates
Jeremy Chapman, M. Burak Erdogan, Derrick Hart +2
An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold such that whenever , where $E \subse…