Campana points and powerful values of norm forms
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 $m$-full norm over a given Galois extension of $\mathbb{Q}$. 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 Várilly-Alvarado.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.01106
- arXiv:
- arXiv:2009.01106
- Bibcode:
- 2020arXiv200901106S
- Keywords:
-
- Mathematics - Number Theory;
- Mathematics - Algebraic Geometry;
- 14G05 (primary);
- 11D45;
- 14G10;
- 11D57 (secondary)
- E-Print:
- 37 pages