English

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 mm-full norm over a given Galois extension of Q\mathbb{Q}. 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

R2 v1 2026-06-23T18:16:11.306Z