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…

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

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