This book is a self-contained account of the one- and
two-dimensional van der Corput method and its use in estimating
exponential sums. These arise in many problems in analytic number
theory. It is the first cohesive account of much of this material
and will be welcomed by graduates and professionals in analytic
number theory. The authors show how the method can be applied to
problems such as upper bounds for the Riemann-Zeta function. the
Dirichlet divisor problem, the distribution of square free numbers,
and the Piatetski-Shapiro prime number theorem.
General
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