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EnglishFor every positive integer n and every δ∈[0,1], let B(n,δ) denote the probabilistic model in which a random set A⊆1,…,n is constructed by choosing independently every element of 1,…,n with probability δ. Moreover, let (uk)k≥0 be an integer sequence satisfying uk=a1uk−1+a2uk−2, for every integer k≥2, where u0=0, u1≠0, and a1,a2 are fixed nonzero integers; and let α and β, with |α|≥|β|, be the two roots of the polynomial X2−a1X−a2. Also, assume that α/β is not a root of unity. We prove that, as δn/logn→+∞, for every A in B(n,δ) we have loglcm(ua:a∈A)∼[Formula presented]⋅n2 with probability 1−o(1), where lcm denotes the lowest common multiple, Li2 is the dilogarithm, and the factor involving δ is meant to be equal to 1 when δ=1. This extends previous results of Akiyama, Tropak, Matiyasevich, Guy, Kiss and Mátyás, who studied the deterministic case δ=1, and is motivated by an asymptotic formula for lcm(A) due to Cilleruelo, Rué, Šarka, and Zumalacárregui.
On the l.c.m. of random terms of binary recurrence sequences / Sanna, C.. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - STAMPA. - 213(2020), pp. 221-231.
| Titolo: | On the l.c.m. of random terms of binary recurrence sequences | |
| Autori: | ||
| Data di pubblicazione: | 2020 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jnt.2019.12.004 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| temp.pdf | 2. Post-print / Author's Accepted Manuscript |  | Embargo: 20/01/2022 Richiedi una copia | |
| On the l.c.m. of random terms of binary recurrence sequences_2020.pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2818859
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