Divisor problem in special sets of Gaussian integers
Journal Title: Карпатські математичні публікації - Year 2016, Vol 8, Issue 2
Abstract
Let $A_1$ and $A_2$ be fixed sets of gaussian integers. We denote by $\tau_{A_1, A_2}(\omega)$ the number of representations of $\omega$ in form $\omega=\alpha\beta$, where $\alpha \in A_1, \beta \in A_2$. We construct the asymptotical formula for summatory function $\tau_{A_1, A_2}(\omega)$ in case, when $\omega$ lie in the arithmetic progression, $A_1$ is a fixed sector of complex plane, $A_2=\mathbb{Z}[i]$.
Authors and Affiliations
O. Savastru
Keywords
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- DOI 10.15330/cmp.8.2.305-312
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