In analytic number theory a large number of problems can be "reduced" to problems involving the estimation of exponential sums in one or several variables. This

A Van der Corput exponential sum is S = exp (2 i f(m)) where m has size M, the function f(x) has size T and = (log M) / log T 1. There are different bounds for

The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Four

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 prob