On the square-free representation function of a norm form and nilsequences

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.

26 pages; revision taking into account referee's comments

References in corpus (1)

• On the fibration method for zero-cycles and rational points

Cited by in corpus (7)

• On the fibration method for zero-cycles and rational points
• Campana points and powerful values of norm forms
• Rational points on fibrations with few non-split fibres
• Strong approximation for a family of norm varieties
• A consequence of the factorisation theorem for polynomial orbits on nilmanifolds
• On the fibration method for rational points
• Polynomials represented by norm forms via the beta sieve