4 papers
math.NT2026
On the asymptotic behavior of the integral T(x)
Mihoub Bouderbala, Meselem Karras
In this paper, we estimate the integral T(x) mentioned in the title, where {t} denotes the fractional part of the real number t, and x is any positive real number.
math.NT2026
On the Mean Value of a Weighted Composite Arithmetic Function
Mihoub Bouderbala
The primary objective of this paper is to employ methods from analytic number theory to investigate the mean value properties of a composite function involving the Dirichlet diviso…
math.NT2025
On certain sums involving the largest prime factor over integer sequences
Mihoub Bouderbala
Given an integer , its prime factorization is expressed as . We define the function as the smallest positive integer such that i…
math.NT2022
On a sum of a multiplicative function linked to the divisor function over the set of integers B-multiple of 5
Mihoub Bouderbala
Let and be the numbers of divisors and the numbers of unitary divisors of the integer . In this paper, we prove that \[ \underset{n\in\mathcal{B}}{\und…