Campana points and powerful values of norm forms
Number Theory
2022-02-01 v2 Algebraic Geometry
Abstract
We give an asymptotic formula for the number of weak Campana points of bounded height on a family of orbifolds associated to norm forms for Galois extensions of number fields. From this formula we derive an asymptotic for the number of elements with -full norm over a given Galois extension of . We also provide an asymptotic for Campana points on these orbifolds which illustrates the vast difference between the two notions, and we compare this to the Manin-type conjecture of Pieropan, Smeets, Tanimoto and V\'arilly-Alvarado.
Keywords
Cite
@article{arxiv.2009.01106,
title = {Campana points and powerful values of norm forms},
author = {Sam Streeter},
journal= {arXiv preprint arXiv:2009.01106},
year = {2022}
}
Comments
37 pages; minor revisions; to appear in Mathematische Zeitschrift