Add to ORKGAbstract. We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory. 1
We prove a new bound on a version of the sum-product problem studied by Chang. By introducing sever...
We derive a new class of sum rules for products of Bessel functions of the first kind. Using standa...
We prove various results on the exponential sum over k-free numbers. As an application, we solve for...
Abstract. We give a general version of cancellation in exponential sums that arise as sums of produc...
One contribution of 8 to a Theo Murphy meeting issue ‘Number fields and function fields: coalescence...
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 20...
We introduce a new comparison principle for exponential sums over finite fields in order to study "s...
Summary This is a brief account of recent developments in the theory of exponen-tial sums and on met...
The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many prod...
We state and discuss various problems in the general area of arithmetic combinatorics and recent dev...
AbstractAn expression for the number of times a certain trace function associated with a Kloosterman...
This thesis establishes new quantitative results in several problems relating to the sum-product phe...
We obtain several versions of the sum-product theorem with k-fold sums and product sets. We also giv...
Abstract. We show that there is significant cancellation in certain exponential sums over small mult...
AbstractLet PT denote the orthogonal projection of L2(R1, dΔ) onto the space of entire functions of ...
We prove a new bound on a version of the sum-product problem studied by Chang. By introducing sever...
We derive a new class of sum rules for products of Bessel functions of the first kind. Using standa...
We prove various results on the exponential sum over k-free numbers. As an application, we solve for...
Abstract. We give a general version of cancellation in exponential sums that arise as sums of produc...
One contribution of 8 to a Theo Murphy meeting issue ‘Number fields and function fields: coalescence...
These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 20...
We introduce a new comparison principle for exponential sums over finite fields in order to study "s...
Summary This is a brief account of recent developments in the theory of exponen-tial sums and on met...
The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many prod...
We state and discuss various problems in the general area of arithmetic combinatorics and recent dev...
AbstractAn expression for the number of times a certain trace function associated with a Kloosterman...
This thesis establishes new quantitative results in several problems relating to the sum-product phe...
We obtain several versions of the sum-product theorem with k-fold sums and product sets. We also giv...
Abstract. We show that there is significant cancellation in certain exponential sums over small mult...
AbstractLet PT denote the orthogonal projection of L2(R1, dΔ) onto the space of entire functions of ...
We prove a new bound on a version of the sum-product problem studied by Chang. By introducing sever...
We derive a new class of sum rules for products of Bessel functions of the first kind. Using standa...
We prove various results on the exponential sum over k-free numbers. As an application, we solve for...