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

Lilian Matthiesen

Type: Article

Publication Date: 2015-11-11

Citations: 12

DOI: https://doi.org/10.1017/s1474748015000389

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.

Locations

Journal of the Institute of Mathematics of Jussieu - View
arXiv (Cornell University) - View - PDF
DataCite API - View

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Works That Cite This (12)

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+ PDF Chat	Rational points and zero-cycles on rationally connected varieties over number fields	2016	Olivier Wittenberg
+ PDF Chat	Rational points and zero-cycles on rationally connected varieties over number fields	2018	Olivier Wittenberg
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+ PDF Chat	Rational points and zero-cycles on rationally connected varieties over number fields	2018	Olivier Wittenberg
+ PDF Chat	Rational points on fibrations with few non-split fibres	2022	Yonatan Harpaz Dasheng Wei Olivier Wittenberg
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+	Campana points and powerful values of norm forms	2020	Sam Streeter
+	On the fibration method for rational points	2019	Dasheng Wei
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+	Norm forms for arbitrary number fields as products of linear polynomials	2017	T. D. Browning Lilian Matthiesen
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+	On the quantitative distribution of polynomial nilsequences - erratum	2013	Ben Green Terence Tao
+ PDF Chat	An inverse theorem for the Gowers $U^{s+1}[N]$-norm	2011	Tamar Ziegler Terence Tao Ben Green