Exponential sums and the Riemann zeta function v

A Van der Corput exponential sum is S = Σ exp (2 π i f(m)) where m has size M, the function f(x) has size T and α = (log M) / log T 0. 2000 Mathematics Subject Classification 11L07 (primary), 11M06, 11P21, 11J54 (secondary).