52 citations · 222 across the 27 of their papers we have counts for
5 papers · 1 filter
On growth in an abstract plane
Nick Gill, H. A. Helfgott, Misha Rudnev
There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over or , geometric statements on growth often…
New sum product type estimates
Sergei V. Konyagin, Misha Rudnev
New lower bounds involving sum, difference, product, and ratio sets for a set $A\subset \C$ are given. The estimates involving the sum set match, up to constants, the one obtained…
On the number of classes of triangles determined by points in
Misha Rudnev
Let be a set of points in the Euclidean plane, where a positive proportion of points lies off a single straight line. This note points out two facts concerning the number o…
Areas of triangles and Beck's theorem in planes over finite fields
Alex Iosevich, Misha Rudnev, Yujia Zhai
It is shown that any subset of a plane over a finite field $\F_q$, of cardinality determines not less than distinct areas of triangles, moreover once ca…
On the Minkowski distances and products of sum sets
Oliver Roche-Newton, Misha Rudnev
Given two points in the real plane, the signed area of the rectangle with the diagonal equals the square of the Minkowski distance between the points . We prove t…