Additive combinatorics is the theory of counting additive structures in sets. This theory has
seen exciting developments and dramatic changes in direction in recent years thanks to its …

A randomness extractor is an algorithm which extracts randomness from a low-quality
random source, using some additional truly random bits. We construct new extractors which …

The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

This is a survey of pseudorandomness, the theory of efficiently generating objects that" look
random" despite being constructed using little or no randomness. This theory has …

During the past two decades there has been active interplay between geometric measure
theory and Fourier analysis. This book describes part of that development, concentrating on …

We study the dimension of self-similar sets and measures on the line. We show that if the
dimension is less than the generic bound of min {1, s}, where s is the similarity dimension …

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

A Kakeya set is a subset of $\mathbb {F}^ n $, where $\mathbb {F} $ is a finite field of $ q $
elements, that contains a line in every direction. In this paper we show that the size of every …

We show that every subset of SL_2(Z/pZ) grows rapidly when it acts on itself by the group
operation. It follows readily that, for every set of generators A of SL_2(Z/pZ), every element of …

In this paper we establish new estimates on sum-product sets and certain exponential sums
in finite fields of prime order. Our first result is an extension of the sum-product theorem from …