Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T22:38:11.706Z Has data issue: false hasContentIssue false
  • English
  • Français

A Fourth Derivative Test for Exponential Sums

Published online by Cambridge University Press:  04 December 2007

O. Robert  and
P. Sargos
O. Robert
Affiliation:
Institut Elie Cartan, Université Henri Poincaré – Nancy I, BP 239, 54 506 Vandoeuvre-lès-Nancy Cedex, France. E-mail: robert@iecn.u-nancy.fr
P. Sargos
Affiliation:
Institut Elie Cartan, Université Henri Poincaré – Nancy I, BP 239, 54 506 Vandoeuvre-lès-Nancy Cedex, France. E-mail: sargos@iecn.u-nancy.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give an upper bound for the exponential sum [sum ]Mm=1 e2iπf(m) in terms of M and λ, where λ 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.

Keywords

exponential sumsdiophantine systems
Type
Research Article
Information
Compositio Mathematica , Volume 130 , Issue 3 , February 2002 , pp. 275 - 292
Copyright
© 2002 Kluwer Academic Publishers