Meselem Karras

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20222026

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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

Note on Fractional Sums with Fixed GCD

Meselem Karras

We investigate fractional sums of arithmetic functions over products of two or three integers, with emphasis on fixed greatest common divisors and multiplicative weights. Let $f$ b…

math.NT2026

On the Mean Value of $D_{k} (n)$ in Arithmetic Progressions

Meselem Karras

Let $k \geq 2$ be a fixed integer. We define the multiplicative function $D_{k} (n) = d_{k} (n) / d_{k}^{*} (n)$ , such that $d_{k} (n)$ is the Piltz divisor function and $d_{k}^{*} (n) = k^{ω (n)}$ is it…

math.NT2024

Hyperbolic summation involving certain arithmetic functions and the integer part function

Meselem Karras

Let f be an arithmetic function satisfying certain conditions. In this paper, we give an asymptotic formula for the sum \[\sum_{n_1 n_2 \cdots n_r \leq x} f\left(\left\lfloor \frac…

math.NT2022

Hyperbolic Summation for Fractional Sums

Meselem Karras, Ling Li, Joshua Stucky

Let $f (n)$ be an arithmetic function with $f (n) ≪ n^{α}$ for some $α \in [0, 1)$ and let $⌊ . ⌋$ denote the integer part function. In this paper, we evaluate asymptoticall…

math.NT2022

Hyperbolic summation involving the function $Ω (n)$ and lcm

Meselem Karras

We study the sum $\sum_{ab c \leq x} Ω ([a, b, c])$ , where $Ω (n)$ denotes the number of distinct prime divisors of $n \in Z_{\geq 1}$ , counted with multiplicity, and where $(a…

math.NT2022

Asymptotic formula for the multiplicative function $\frac{d ( n )}{k ^{ω (n)}}$

Meselem Karras

For a fixed integer $k$ , we define the multiplicative function \[D_{k,ω}(n) := \frac{d(n)}{k^{ω(n)}}, \]where $d (n)$ is the divisor function and $ω (n)$ is the number of distinct pr…

On the asymptotic behavior of the integral T(x)

Note on Fractional Sums with Fixed GCD

On the Mean Value of Dk​(n) in Arithmetic Progressions

Hyperbolic summation involving certain arithmetic functions and the integer part function

Hyperbolic Summation for Fractional Sums

Hyperbolic summation involving the function Ω(n) and lcm

Asymptotic formula for the multiplicative function kω(n)d(n)​

On the Mean Value of $D_{k} (n)$ in Arithmetic Progressions

Hyperbolic summation involving the function $Ω (n)$ and lcm

Asymptotic formula for the multiplicative function $\frac{d ( n )}{k ^{ω (n)}}$