52 citations · 222 across the 27 of their papers we have counts for
39 papers
Multiplicative Subgroups of Prime Fields Are Not Sumsets
Misha Rudnev, Fred Tyrrell
Let be a proper multiplicative subgroup, and suppose that for some . We prove that either one of the summands is a sin…
The sum-product problem for integers with few prime factors
Brandon Hanson, Misha Rudnev, Ilya Shkredov +1
It was asked by E. Szemerédi if, for a finite set , one can improve estimates for , under the constraint that all integers involved ha…
Higher Convexity and Iterated Second Moment Estimates
Peter J. Bradshaw, Brandon Hanson, Misha Rudnev
We prove bounds for the number of solutions to over -element sets of reals, which are sufficiently convex or near-convex. A near-conv…
An update on the sum-product problem
Misha Rudnev, Sophie Stevens
We improve the best known sum-product estimates over the reals. We prove that \[ \max(|A+A|,|AA|)\geq |A|^{\frac{4}{3} + \frac{2}{1167} - o(1)}\,, \] for a finite $A\subset \mathbb…
Higher convexity and iterated sum sets
Brandon Hanson, Oliver Roche-Newton, Misha Rudnev
Let be a smooth real function with strictly monotone first derivatives. We show that for a finite set , with , $|2^kf(A)-(2^k-1)f(A)|\gg_k |A|^{k+1-o(1)}…
On the Pinned Distances Problem in Positive Characteristic
Brendan Murphy, Giorgis Petridis, Thang Pham +2
We study the Erd\H os-Falconer distance problem for a set , where is a field of positive characteristic . If and th…