The density of the terms in an elliptic divisibility sequence having a fixed G.C.D. with their indices

Autor:	Seoyoung Kim
Rok vydání:	2020
Předmět:	Combinatorics Algebra and Number Theory Trace (linear algebra) Integer Distribution (number theory) 010102 general mathematics Natural density 010103 numerical & computational mathematics 0101 mathematics Elliptic divisibility sequence Möbius function 01 natural sciences Mathematics
Zdroj:	Journal of Number Theory. 207:22-41
ISSN:	0022-314X
DOI:	10.1016/j.jnt.2019.06.014
Popis:	Let D = ( D n ) n ≥ 1 be an elliptic divisibility sequence associated to the pair ( E , P ) . For a fixed integer k, we define A E , k = { n ≥ 1 : gcd ⁡ ( n , D n ) = k } . We give an explicit structural description of A E , k . Also, we explain when A E , k has positive asymptotic density using bounds related to the distribution of trace of Frobenius of E. Furthermore, we obtain an explicit density for A E , k using the Mobius function.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::eaa5b06dc679e367bb242b194485138d https://doi.org/10.1016/j.jnt.2019.06.014 Zobrazit plný text záznamu Full Text from ScienceDirect