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Rational points on linear slices of diagonal hypersurfaces

Part of: Diophantine equations Exponential sums and character sums Additive number theory; partitions

Published online by Cambridge University Press:  11 January 2016

Jörg Brüdern  and
Olivier Robert
Jörg Brüdern
Affiliation:
Mathematisches Institut, D-37073 Göttingen, Germany, bruedern@uni-math.gwdg.de
Olivier Robert
Affiliation:
Université de Lyon and Université de Saint-Etienne, Institut Camille Jordan CNRS UMR 5208, F-42000 Saint-Etienne, France, olivier.robert@univ-st-etienne.fr
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Abstract

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An asymptotic formula is obtained for the number of rational points of bounded height on the class of varieties described in the title line. The formula is proved via the Hardy-Littlewood method, and along the way we establish two new results on Weyl sums that are of some independent interest.

MSC classification

Secondary: 11D45: Counting solutions of Diophantine equations 11L15: Weyl sums 11P55: Applications of the Hardy-Littlewood method
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 218 , June 2015 , pp. 51 - 100
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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