On the least common multiple of several random integers

DOI10.1016/j.jnt.2019.03.017zbMath1473.11155arXiv1901.03002OpenAlexW2909458492WikidataQ128038727 ScholiaQ128038727MaRDI QIDQ2315980

Alin Bostan, Kilian Raschel, Alexander Marynych

Publication date: 26 July 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.03002

zbMATH Keywords

convergence in distributionleast common multipleprime productstrimmed sums of geometric laws

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Asymptotic results on arithmetic functions (11N37) Arithmetic functions; related numbers; inversion formulas (11A25) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Arithmetic functions in probabilistic number theory (11K65)

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Cites Work

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• Counting \(r\)-tuples of positive integers with \(k\)-wise relatively prime components
• The least common multiple of random sets of positive integers
• On the average value of the least common multiple of \(k\) positive integers
• Logarithmic combinatorial structures: A probabilistic approach
• Precision calculation of distributions for trimmed sums
• Approximation of singular series and automata
• On the probability that \(k\) positive integers are relatively prime
• On the number of solutions to a Diophantine equation
• ON THE MERTENS–CESÀRO THEOREM FOR NUMBER FIELDS
• On the density of coprime m-tuples over holomorphy rings
• THE PROBABILITY THAT RANDOM POSITIVE INTEGERS ARE k-WISE RELATIVELY PRIME
• Limit theorems for the least common multiple of a random set of integers
• Limit Theorems for Empirical Density of Greatest Common Divisors
• Sur un probl?me de g?om?trie diophantienne lin?aire. I. Poly?dres et r?seaux.