Campana points and powerful values of norm forms

DOI10.1007/S00209-021-02922-4arXiv2009.01106MaRDI QIDQ6348246

Sam Streeter

Publication date: 2 September 2020

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 $mathbbQ$. 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.

Mathematics Subject Classification ID

Rational points (14G05) Counting solutions of Diophantine equations (11D45) Varieties over global fields (11G35) Heights (11G50) Multiplicative and norm form equations (11D57)

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