Divisibility properties of random samples of integers

DOI10.1007/s13398-020-00960-xzbMath1458.11127OpenAlexW3106700732MaRDI QIDQ2220962

Pablo Fernández, José Lúis Fernandez Perez

Publication date: 25 January 2021

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-020-00960-x

zbMATH Keywords

asymptotic normalitywaiting timesrandom walkdivisibilityvisible pointscoprimality and pairwise coprimalitydistribution and moments of gcd and lcmrandom samples of integers

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Asymptotic results on arithmetic functions (11N37) Arithmetic functions; related numbers; inversion formulas (11A25) Arithmetic functions in probabilistic number theory (11K65)

Related Items (7)

Generalized visibility of lattice points in higher dimensions ⋮ On the distribution of the \(\mathrm{lcm}\) of \(k\)-tuples and related problems ⋮ Multivariate multiplicative functions of uniform random vectors in large integer domains ⋮ Divisibility properties of polynomial expressions of random integers ⋮ Approximation formulas and inequalities for the Euler-Mascheroni constant ⋮ On the degree of the GCD of random polynomials over a finite field ⋮ Central limit theorem for the least common multiple of a uniformly sampled \(m\)-tuple of integers

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
• Ergodic properties of visible lattice points
• Visible lattice points and the chromatic zeta function of a graph
• On normal approximations of distributions in terms of dependency graphs
• On the average value of the least common multiple of \(k\) positive integers
• Visibility in the plane
• On the distribution of the greatest common divisor of Gaussian integers
• Number of irreducible polynomials and pairs of relatively prime polynomials in several variables over finite fields
• The probability that random algebraic integers are relatively \(r\)-prime
• Normal convergence by higher semi-invariants with applications to sums of dependent random variables and random graphs
• Probability, information theory, and prime number theory
• Birthday paradox, coupon collectors, caching algorithms and self- organizing search
• The probability that \(k\) positive integers are relatively \(r\)-prime
• A pentagonal number sieve
• The probability of two integers to be co-prime, revisited -- on the behavior of CLT-scaling limit
• Diffraction from visible lattice points and \(k\)th power free integers
• Distribution of lattice points visible from the origin
• Visible lattice points in random walks
• Tuples of polynomials over finite fields with pairwise coprimality conditions
• Number theory in science and communication. With applications in cryptography, physics, digital information, computing, and self- similarity.
• General asymptotic estimates for the coupon collector problem
• On an involution concerning pairs of polynomials over \(\mathbb{F}_2\)
• Visible lattice points along curves
• On the probability that two random integers are coprime
• On the least common multiple of several random integers
• Entropy and diffraction of the \(k\)-free points in \(n\)-dimensional lattices
• On the probability that \(k\) positive integers are relatively prime
• ON THE MERTENS–CESÀRO THEOREM FOR NUMBER FIELDS
• THE PROBABILITY THAT RANDOM POSITIVE INTEGERS ARE k-WISE RELATIVELY PRIME
• Asymptotic normality and greatest common divisors
• Maximum GCD Among Pairs of Random Integers
• The coupon-collector problem revisited — a survey of engineering problems and computational methods
• The Asymptotic Density of Some k-Dimensional Sets
• Arithmetical Functions of a Greatest Common Divisor. I
• Counting tuples restricted by coprimality conditions
• Seeing Dots: Visibility of Lattice Points
• The Probability of Relatively Prime Polynomials
• Asymptotic normality of some Graph-Related statistics
• Rates of Poisson convergence for U-statistics
• On the probability that integers chosen according to the binomial distribution are relative prime
• Short distances, flat triangles and Poisson limits
• Lattice Point Visibility on Generalized Lines of Sight
• The probability that two random integers are coprime
• THE DENSITY OF -WISE RELATIVELY -PRIME ALGEBRAIC INTEGERS
• Asymptotic behaviour of some infinite products involvingprime numbers
• The probability that ideals in a number ring are k-wise relatively r-prime
• On certain sums concerning the gcd’s and lcm’s of k positive integers
• Limit theorems for the least common multiple of a random set of integers
• Multiplicative Arithmetic Functions of Several Variables: A Survey
• Limit Theorems for Empirical Density of Greatest Common Divisors
• Lattice point visibility on power functions
• Degree distribution of the greatest common divisor of polynomials over 𝔽_q
• Patterns of Visible and Nonvisible Lattice Points

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