Difference Sets and Polynomials

Neil Lyall, Alex Rice

We provide upper bounds on the largest subsets of $\{1,2,\dots ,N\}$ with no differences of the form $h_1(n_1)+\cdots +h_{\ell }(n_{\ell })$ with $n_i\in \mathbb{N}$ or $h_1(p_1)+\cdot…