52 citations · 222 across the 27 of their papers we have counts for
4 papers · 1 filter
On growth rate in , the affine group and sum-product type implications
Misha Rudnev, Ilya D. Shkredov
This paper aims to study in more depth the relation between growth in matrix groups and over a field by multiplication…
Stronger sum-product inequalities for small sets
Misha Rudnev, George Shakan, Ilya Shkredov
Let be a field and a finite be sufficiently small in terms of the characteristic of if . We strengthen the "threshold" sum-product inequality $$|AA|^3…
Point-plane incidences and some applications in positive characteristic
Misha Rudnev
The point-plane incidence theorem states that the number of incidences between points and planes in the projective three-space over a field , is $$O\left(m\sqrt{n}…
On the restriction problem for discrete paraboloid in lower dimension
Misha Rudnev, Ilya D. Shkredov
We apply geometric incidence estimates in positive characteristic to prove the optimal Fourier extension estimate for the paraboloid in the four-dimensional vector sp…