University of Pecs

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19972026

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math.NT2025

Generalizations of Euler's $φ$ -function with respect to systems of polynomials of several variables

Norbert Csizmazia, László Tóth

We introduce a new generalization of Euler's $φ$ -function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related…

math.NT2022★ 2 cited

Estimates for $k$ -dimensional spherical summations of arithmetic functions of the GCD and LCM

Randell Heyman, László Tóth

Let $k \geq 2$ be a fixed integer. We consider sums of type $\sum_{n_{1}^{2} + \dots + n_{k}^{2} \leq x} F (n_{1}, \dots, n_{k})$ , taken over the $k$ -dimensional spherical region $\{(n_1,\ldots,n_k)\i…

math.NT2022★ 11 cited

Hyperbolic summation for functions of the GCD and LCM of several integers

Randell Heyman, László Tóth

Let $k \geq 2$ be a fixed integer. We consider sums of type $\sum_{n_{1} \dots n_{k} \leq x} F (n_{1}, \dots, n_{k})$ , taken over the hyperbolic region $\{(n_1,\ldots,n_k)\in {\Bbb N}^k: n_1\cdo…

math.NT2021★ 4 cited

Proofs, generalizations and analogs of Menon's identity: a survey

László Tóth

Menon's identity states that for every positive integer $n$ one has $\sum (a - 1, n) = φ (n) τ (n)$ , where $a$ runs through a reduced residue system (mod $n$ ), $(a - 1, n)$ stands for the…

math.NT2021★ 2 cited

Menon-type identities concerning subsets of the set ${1, 2, \dots, n}$

László Tóth

We prove certain Menon-type identities associated with the subsets of the set ${1, 2, \dots, n}$ and related to the functions $f$ , $f_{k}$ , $Φ$ and $Φ_{k}$ , defined and investigated by…

math.NT2021★ 3 cited

Additive arithmetic functions meet the inclusion-exclusion principle: Asymptotic formulas concerning the GCD and LCM of several integers

Olivier Bordellès, László Tóth

We obtain asymptotic formulas for the sums $\sum_{n_{1}, \dots, n_{k} \leq x} f ((n_{1}, \dots, n_{k}))$ and $\sum_{n_{1}, \dots, n_{k} \leq x} f ([n_{1}, \dots, n_{k}])$ involving the gcd and lcm of the i…

Generalizations of Euler's φ-function with respect to systems of polynomials of several variables

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