Higher Convexity and Iterated Second Moment Estimates

Peter J. Bradshaw, Brandon Hanson, Misha Rudnev

We prove bounds for the number of solutions to $$a_1+\cdots +a_k=a_1^{\prime }+\cdots +a_k^{\prime }$$ over $N$-element sets of reals, which are sufficiently convex or near-convex. A near-conv…