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Keywords:
arithmetic function; greatest common divisor
arithmetic function; greatest common divisor
Summary:
Let $x>1$ and $\alpha $, $\beta $ be positive integers such that $1< \alpha <\beta $. We consider sums of type $\sum _{m^\alpha n^\beta \leq x}f(\gcd (m, n)),$ taken over the region $\{ (m, n)\in \mathbb {N}^2\colon m^\alpha n^\beta \leq x\}$, where $f$ belongs to certain classes of arithmetic functions and $\gcd (m, n)$ denotes the greatest common divisor of the integers $m$, $n$.
References:
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