The method of exponential sums is a general method enabling the
solution of a wide range of problems in the theory of numbers and
its applications. This volume presents an exposition of the
fundamentals of the theory with the help of examples which show how
exponential sums arise and how they are applied in problems of
number theory and its applications. The material is divided into
three chapters which embrace the classical results of Gauss, and
the methods of Weyl, Mordell and Vinogradov; the traditional
applications of exponential sums to the distribution of fractional
parts, the estimation of the Riemann zeta function; and the theory
of congruences and Diophantine equations. Some new applications of
exponential sums are also included. It is assumed that the reader
has a knowledge of the fundamentals of mathematical analysis and of
elementary number theory.
General
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