J Austral Math Soc Ser A 59 pp304--307, 1995.

A Mean Value Theorem for Exponential Sums

M. N. Huxley

(Received 27 July 1992; revised 5 November 1993)

Abstract

The exponential sum S(x) = åe(f(m + x)) has a mean square size O(M), when m runs through M consecutive integers, f(x) satisfies bounds on the second and third derivatives, and x runs from 0 to 1.

1991 AMS Subject Classification: 11L07

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Authors

M. N. Huxley: School of Mathematics, University of Wales College of Cardiff, 23 Senghenydd Road, Cardiff, Wales CF2 4YH, UK.

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Last Modified: Thu Jan 9 9:04:23 2003