학술논문
A fourth derivative test for exponential sums
Document Type
Working Paper
Source
Compositio Mathematica, 2002, 130 (3), pp.275-292
Subject
Language
Abstract
We give an upper bound for the exponential $\sum_{m=1}^M \exp( 2i\pi f (m))$ in terms of $M$ and $\lambda$, where $\lambda$ is a small positive number which denotes the size of the fourth derivative of the real valued function $f$. The classical van der Corput's exponent 1/14 is improved into 1/13 by reducing the problem to a mean square value theorem for triple exponential sums.