Add to ORKGThese notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains a clean proof of the Bourgain-Katz-Tao theorem on the sum-product phenomenon in F_p. The arguments are essentially extracted from a paper of Bourgain, and I benefitted very much from being in receipt of unpublished course notes of Elon Lindenstrauss. No originality is claimed
We first prove an extension of the Bourgain-Sarnak-Ziegler theorem, relaxing some conditions and giv...
In this note we prove a new estimate on so-called GCD sums (also called G\'{a}l sums), which, for ce...
We examine a family of three-dimensional exponential sums with monomials and provide estimates which...
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 20...
This thesis establishes new quantitative results in several problems relating to the sum-product phe...
The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many prod...
Let Fp be the finite field of a prime order p. Let F: Fp x Fp --> Fp be a function defined by F(x, y...
Summary This is a brief account of recent developments in the theory of exponen-tial sums and on met...
We obtain several versions of the sum-product theorem with k-fold sums and product sets. We also giv...
We introduce a new comparison principle for exponential sums over finite fields in order to study "s...
We state and discuss various problems in the general area of arithmetic combinatorics and recent dev...
In our paper, we introduce a new method for estimating incidences via representation theory. We obta...
Abstract. We give a general version of cancellation in exponential sums that arise as sums of produc...
summary:The sum-product algorithm is a well-known procedure for marginalizing an “acyclic” product f...
One contribution of 8 to a Theo Murphy meeting issue ‘Number fields and function fields: coalescence...
We first prove an extension of the Bourgain-Sarnak-Ziegler theorem, relaxing some conditions and giv...
In this note we prove a new estimate on so-called GCD sums (also called G\'{a}l sums), which, for ce...
We examine a family of three-dimensional exponential sums with monomials and provide estimates which...
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 20...
This thesis establishes new quantitative results in several problems relating to the sum-product phe...
The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many prod...
Let Fp be the finite field of a prime order p. Let F: Fp x Fp --> Fp be a function defined by F(x, y...
Summary This is a brief account of recent developments in the theory of exponen-tial sums and on met...
We obtain several versions of the sum-product theorem with k-fold sums and product sets. We also giv...
We introduce a new comparison principle for exponential sums over finite fields in order to study "s...
We state and discuss various problems in the general area of arithmetic combinatorics and recent dev...
In our paper, we introduce a new method for estimating incidences via representation theory. We obta...
Abstract. We give a general version of cancellation in exponential sums that arise as sums of produc...
summary:The sum-product algorithm is a well-known procedure for marginalizing an “acyclic” product f...
One contribution of 8 to a Theo Murphy meeting issue ‘Number fields and function fields: coalescence...
We first prove an extension of the Bourgain-Sarnak-Ziegler theorem, relaxing some conditions and giv...
In this note we prove a new estimate on so-called GCD sums (also called G\'{a}l sums), which, for ce...
We examine a family of three-dimensional exponential sums with monomials and provide estimates which...