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• W2909458492 abstract "Let $L_n(k)$ denote the least common multiple of $k$ independent random integers uniformly chosen in ${1,2,ldots ,n}$. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as $ntoinfty$ of $frac{f(L_n(k))}{n^{rk}}$ for a wide class of multiplicative arithmetic functions~$f$ with polynomial growth $r>-1$. Furthermore, we identify the limit as an infinite product of independent random variables indexed by prime numbers. Along the way, we compute the generating function of a trimmed sum of independent geometric laws, occurring in the above infinite product. This generating function is rational; we relate it to the generating function of a certain max-type Diophantine equation, of which we solve a generalized version. Our results extend theorems by ErdH{o}s and Wintner (1939), Fern'{a}ndez and Fern'{a}ndez (2013) and Hilberdink and T'{o}th (2016)." @default.
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• W2909458492 date "2019-11-01" @default.
• W2909458492 modified "2023-09-25" @default.
• W2909458492 title "On the least common multiple of several random integers" @default.
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• W2909458492 doi "https://doi.org/10.1016/j.jnt.2019.03.017" @default.
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