Meselem Karras

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20222026

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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…

Hyperbolic Summation for Fractional Sums

Hyperbolic summation involving the function Ω(n) and lcm

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

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

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