Matches in SemOpenAlex for { <https://semopenalex.org/work/W4301457974> ?p ?o ?g. }
Showing items 1 to 48 of
48
with 100 items per page.
- W4301457974 abstract "Let $(u_n)_{n geq 0}$ be a non-degenerate Lucas sequence, given by the relation $u_n=a_1 u_{n-1}+a_2 u_{n-2}$. Let $ell_u(m)=lcm(m, z_u(m))$, for $(m,a_2)=1$, where $z_u(m)$ is the rank of appearance of $m$ in $u_n$. We prove that $$sum_{substack{m>x (m,a_2)=1}}frac{1}{ell_u(m)}leq exp(-(1/sqrt{6}-varepsilon+o(1))sqrt{(log x)(log log x)}),$$ when $x$ is sufficiently large in terms of $varepsilon$, and where the $o(1)$ depends on $u$. Moreover, if $g_u(n)=gcd(n,u_n)$, we will show that for every $kgeq 1$, $$sum_{nleq x}g_u(n)^{k}leq x^{k+1}exp(-(1+o(1))sqrt{(log x)(log log x)}),$$ when $x$ is sufficiently large and where the $o(1)$ depends on $u$ and $k$. This gives a partial answer to a question posed by C. Sanna. As a by-product, we derive bounds on $#{nleq x: (n, u_n)>y}$, at least in certain ranges of $y$, which strengthens what already obtained by Sanna. Finally, we start the study of the multiplicative analogous of $ell_u(m)$, finding interesting results." @default.
- W4301457974 created "2022-10-05" @default.
- W4301457974 creator A5061540415 @default.
- W4301457974 date "2018-05-06" @default.
- W4301457974 modified "2023-09-25" @default.
- W4301457974 title "An Upper Bound for the Moments of a G.C.D. related to Lucas Sequences" @default.
- W4301457974 doi "https://doi.org/10.48550/arxiv.1805.02225" @default.
- W4301457974 hasPublicationYear "2018" @default.
- W4301457974 type Work @default.
- W4301457974 citedByCount "0" @default.
- W4301457974 crossrefType "posted-content" @default.
- W4301457974 hasAuthorship W4301457974A5061540415 @default.
- W4301457974 hasBestOaLocation W43014579741 @default.
- W4301457974 hasConcept C114614502 @default.
- W4301457974 hasConcept C121332964 @default.
- W4301457974 hasConcept C134306372 @default.
- W4301457974 hasConcept C164226766 @default.
- W4301457974 hasConcept C2524010 @default.
- W4301457974 hasConcept C33923547 @default.
- W4301457974 hasConcept C42747912 @default.
- W4301457974 hasConcept C77553402 @default.
- W4301457974 hasConcept C90673727 @default.
- W4301457974 hasConceptScore W4301457974C114614502 @default.
- W4301457974 hasConceptScore W4301457974C121332964 @default.
- W4301457974 hasConceptScore W4301457974C134306372 @default.
- W4301457974 hasConceptScore W4301457974C164226766 @default.
- W4301457974 hasConceptScore W4301457974C2524010 @default.
- W4301457974 hasConceptScore W4301457974C33923547 @default.
- W4301457974 hasConceptScore W4301457974C42747912 @default.
- W4301457974 hasConceptScore W4301457974C77553402 @default.
- W4301457974 hasConceptScore W4301457974C90673727 @default.
- W4301457974 hasLocation W43014579741 @default.
- W4301457974 hasLocation W43014579742 @default.
- W4301457974 hasOpenAccess W4301457974 @default.
- W4301457974 hasPrimaryLocation W43014579741 @default.
- W4301457974 hasRelatedWork W2050921239 @default.
- W4301457974 hasRelatedWork W2101620967 @default.
- W4301457974 hasRelatedWork W2147422606 @default.
- W4301457974 hasRelatedWork W2168596199 @default.
- W4301457974 hasRelatedWork W2516428376 @default.
- W4301457974 hasRelatedWork W3034333085 @default.
- W4301457974 hasRelatedWork W4226517247 @default.
- W4301457974 hasRelatedWork W4298276972 @default.
- W4301457974 hasRelatedWork W4308613719 @default.
- W4301457974 hasRelatedWork W4221162730 @default.
- W4301457974 isParatext "false" @default.
- W4301457974 isRetracted "false" @default.
- W4301457974 workType "article" @default.