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MINOR ARC MOMENTS OF WEYL SUMS

Published online by Cambridge University Press:  02 August 2012

M. P. HARVEY
M. P. HARVEY*
Affiliation:
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom e-mail: michael.harvey@rhul.ac.uk
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Abstract

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We obtain an improved bound for the 2k-th moment of a degree k Weyl sum, restricted to a set of minor arcs, when k is small. We then present some applications of this bound to some Diophantine problems, including a case of the Waring–Goldbach problem, and a particular family of Diophantine equations defined as the sum of a norm form and a diagonal form.

Keywords

11L1511P55
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013 , pp. 97 - 113
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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