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Divisibility properties of random samples of integers

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Abstract

This paper is devoted to survey the rich theory, some of it quite recent, concerning the divisibility properties, of various kinds, of random r-tuples of positive integers.

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Notes

  1. Usually attributed to Dirichlet [37]. But also to Cesàro [22, 23], Mertens [74], Sylvester [88], etc. See an interesting historical account in [1].

  2. These asymptotic estimates of moments of gcd are valid also for non-integer q, but we limit ourselves to the integer case.

  3. A completely analogous characterization holds in the k-dimensional lattice; see Theorem 2 in [56].

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  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    José L. Fernández & Pablo Fernández

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Fernández, J.L., Fernández, P. Divisibility properties of random samples of integers. RACSAM 115, 26 (2021). https://doi.org/10.1007/s13398-020-00960-x

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