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An analogue of Van der Corput's A5-process for exponential sums

Part of: Exponential sums and character sums

Published online by Cambridge University Press:  26 February 2010

O. Robert
O. Robert
Affiliation:
Institut Elie Cartan, Université Henri Poincaré—Nancy I, BP 239, 54 506 Vandoeuvre-lès-Nancy Cedex, France. E-mail: [email protected]
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Abstract

A diophantine system is studied from which is deduced an analogue of van der Corput's A5-process in order to bound analytic exponential sums of the form . The saving has now to be taken to the exponent 1/20 instead of 1/32. Our main application is a “ninth derivative test” for exponential sums which is essential for giving new exponent pairs in [3].

MSC classification

Secondary: 11L07: Estimates on exponential sums
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 167 - 183
Copyright
Copyright © University College London 2002

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References

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