The next meeting of the seminar will be held on October 10, 2014 (Friday), at 11:00, in Room 578 of the Institute of Mathematics and Informatics.

A talk on

Kloosterman sums and applications in analytic number theory

will be delivered by Prof. Dojchin Tolev, FMI - Sofia University.

Everybody is invited.

Abstract.
The Kloosterman sums play an important role in analytic number theory.
They were introduced by Kloosterman in 1926 in his investigation of the solvability of Diophantine equations in four variables. Later it turned out that that these sums appear in many other problems, for example in the theory of the Riemann zeta-function. One the main problems is to find nontrivial estimates of the module of these sums. The first estimates were found by Kloosterman and his result was improved by A. Weil in 1946 who used methods from algebraic geometry and found an estimate which cannot be further improved.
In the talk we shall state a series of problems in number theory whose solution is based on the properties of the Kloosterman sums and, we shall try to explain some elementary methods to estimate these sums.