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Asymptotics of arithmetic functions of GCD and LCM of random integers in hyperbolic regions

Abstract : We prove limit theorems for the greatest common divisor and the least common multiple of random integers. While the case of integers uniformly distributed on a hypercube with growing size is classical, we look at the uniform distribution on sublevel sets of multivariate symmetric polynomials, which we call hyperbolic regions. Along the way of deriving our main results, we obtain some asymptotic estimates for the number of integer points in these hyperbolic domains, when their size goes to infinity.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03501402
Contributor : Kilian Raschel Connect in order to contact the contributor
Submitted on : Thursday, December 23, 2021 - 11:40:20 AM
Last modification on : Sunday, June 26, 2022 - 3:28:51 AM

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  • HAL Id : hal-03501402, version 1
  • ARXIV : 2112.11892

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Alexander Iksanov, Alexander Marynych, Kilian Raschel. Asymptotics of arithmetic functions of GCD and LCM of random integers in hyperbolic regions. {date}. ⟨hal-03501402⟩

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