We prove a new upper bound for the number of incidences between points and lines in a
plane over an arbitrary field F, a problem first considered by Bourgain, Katz and Tao …

Sums and products of sets and estimates of rational trigonometric sums in fields of prime
order Page 1 Russian Mathematical Surveys Sums and products of sets and estimates of …

Let $ P:\F\times\F\to\F $ be a polynomial of bounded degree over a finite field $\F $ of large
characteristic. In this paper we establish the following dichotomy: either $ P $ is a moderate …

In a recent work, Kumar, Meka, and Sahai (FOCS 2019) introduced the notion of bounded
collusion protocols (BCPs). BCPs are multiparty communication protocols in which N parties …

We determine which quadratic polynomials in three variables are expanders over an
arbitrary field F F. More precisely, we prove that for a quadratic polynomial f∈ FF x, y, z …

We establish several sum–product estimates over finite fields that involve polynomials and
rational functions. First,| f (A)+ f (A)+| AA| is substantially larger than| A| for an arbitrary …

In 2005 Bourgain gave the first explicit construction of a two‐source extractor family with min‐
entropy rate less than 1/2. His approach combined Fourier analysis with innovative but …

In this paper we provide in F p expanding lower bounds for two variables functions f (x, y) in
connection with the product set or the sumset. The sum–product problem has been …

Let the set of positive integers be colored in an arbitrary way in finitely many colors (a “finite
coloring”). Is it true that, in this case, there are x, y∈ ℤ such that x+ y, xy, and x have the …

In this note, we use methods from spectral graph theory to obtain bounds on the number of
incidences between $ k $-planes and $ h $-planes in $\mathbb {F} _q^ d $, which …