4 citations · 7 across the 3 of their papers we have counts for
5 papers
Improved Bounds on Sarkozy's Theorem for Quadratic Polynomials
Mariah Hamel, Neil Lyall, Alex Rice
We extend the best known bound on the largest subset of {1,2,...,N} with no square differences to the largest possible class of quadratic polynomials.
Arithmetic Structure in Sparse Difference Sets
Mariah Hamel, Neil Lyall, Katherine Thompson +1
Using a slight modification of an argument of Croot, Ruzsa and Schoen we establish a quantitative result on the existence of a dilated copy of any given configuration of integer po…
On Sums of Sets of Primes with Positive Relative Density
Karsten Chipeniuk, Mariah Hamel
In this paper we show that if is a subset of the primes with positive relative density , then must have positive upper density $C_1δe^{-C_2(\log(1/δ))^{2/3}(\log\log(1…
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,…
Arithmetic structures in random sets
Mariah Hamel, Izabella Laba
We extend two well-known results in additive number theory, Sárközy's theorem on square differences in dense sets and a theorem of Green on long arithmetic progressions in sumsets,…