Abstract
AbstractWe 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 $$\mathbb {Q}$$
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.
Publisher
Springer Science and Business Media LLC
Reference33 articles.
1. Abramovich, D.: Birational Geometry for Number Theorists Arithmetic Geometry, Clay Mathematical Proceedings, vol. 8, pp. 335–373. American Mathematical Society, Providence (2009)
2. Abramovich, D., Várilly-Alvarado, A.: Campana points, Vojta’s conjecture, and level structures on semistable abelian varieties. J. Théor. Nombres Bordeaux 30(2), 525–532 (2018)
3. Batyrev, V., Tschinkel, Y.: Rational points of bounded height on compactifications of anisotropic tori. Int. Math. Res. Not. no. 12, 591–635 (1995)
4. Bourqui, D.: Fonction zêta des hauteurs des variétés toriques non déployées. Mem. AMS 211, 20 (2011)
5. Browning, T., Van Valckenborgh, K.: Sums of three squareful numbers. Exp. Math. 21(2), 204–211 (2012)
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献