Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772604 | Journal of Number Theory | 2017 | 13 Pages |
Abstract
Let F and G be linear recurrences over a number field K, and let R be a finitely generated subring of K. Furthermore, let N be the set of positive integers n such that G(n)â 0 and F(n)/G(n)âR. Under mild hypothesis, Corvaja and Zannier proved that N has zero asymptotic density. We prove that #(Nâ©[1,x])âªxâ
(logâ¡logâ¡x/logâ¡x)h for all xâ¥3, where h is a positive integer that can be computed in terms of F and G. Assuming the Hardy-Littlewood k-tuple conjecture, our result is optimal except for the term logâ¡logâ¡x.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Carlo Sanna,