Estimates for \(k\)-dimensional spherical summations of arithmetic functions of the GCD and LCM

DOI10.1007/978-3-031-31617-3_11MaRDI QIDQ6606729

Randell Heyman, László Tóth

Publication date: 17 September 2024

zbMATH Keywords

greatest common divisorasymptotic formulaleast common multiplearithmetic functionspherical summationnumber of integer lattice points in a sphereWintner's mean value theorem

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Cites Work

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• On the average value of the least common multiple of \(k\) positive integers
• On the primitive circle problem
• On multivariable averages of divisor functions
• On certain sums of arithmetic functions involving the GCD and LCM of two positive integers
• Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function
• Additive arithmetic functions meet the inclusion-exclusion principle: asymptotic formulas concerning the GCD and LCM of several integers
• Visible lattice points in the sphere
• Error term concerning number of subgroups of group \(\mathbb{Z}_m \times \mathbb{Z}_n\) with \(m^2 + n^2 \le x\)
• Estimation of multiple sums of arithmetical functions
• The Circle Problem of Gauss and the Divisor Problem of Dirichlet—Still Unsolved
• Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables
• A survey of the alternating sum-of-divisors function
• On certain sums concerning the gcd’s and lcm’s of k positive integers
• Multiplicative Arithmetic Functions of Several Variables: A Survey
• Hyperbolic summation for functions of the GCD and LCM of several integers

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