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) = 0 and F(n)/G(n) ∈ R. Under mild hypothesis, Corvaja and Zannier proved that N has zero asymptotic density. We prove that #(N ∩ [1, x]) x · (log log x/ log x)h for all x ≥ 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 log log x
Distribution of integral values for the ratio of two linear recurrences / Sanna, Carlo. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - STAMPA. - 180(2017), pp. 195-207.
Titolo: | Distribution of integral values for the ratio of two linear recurrences |
Autori: | |
Data di pubblicazione: | 2017 |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jnt.2017.04.015 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
temp.pdf | Articoli principale | 1. Preprint / Submitted Version | Non Pubblico - Accesso privato/ristretto | Visibile a tuttiVisualizza/Apri |
Journal of Number Theory.pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2722597