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ON THE SQUARE-FREE REPRESENTATION FUNCTION OF A NORM FORM AND NILSEQUENCES

Part of: Multiplicative number theory Sequences and sets Arithmetic problems. Diophantine geometry Diophantine equations

Published online by Cambridge University Press:  11 November 2015

Lilian Matthiesen
Lilian Matthiesen*
Affiliation:
Institut de Mathématiques de Jussieu – Paris Rive Gauche, UMR 7586, Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, France (lilian.matthiesen@imj-prg.fr)
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Abstract

We show that the restriction to square-free numbers of the representation function attached to a norm form does not correlate with nilsequences. By combining this result with previous work of Browning and the author, we obtain an application that is used in recent work of Harpaz and Wittenberg on the fibration method for rational points.

Keywords

norm form equationsweak approximationhigher degree uniformitynilsequences

MSC classification

Primary: 14G05: Rational points 11D57: Multiplicative and norm form equations 11B30: Arithmetic combinatorics; higher degree uniformity 11N37: Asymptotic results on arithmetic functions
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 1 , February 2018 , pp. 107 - 135
Copyright
© Cambridge University Press 2015 

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References

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