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Algebra and Discrete Mathematics, 2003, Issue 1, Pages 103–110
(Mi adm373)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
An additive divisor problem in $\mathbb{Z}[i]$
O. V. Savasrtua, P. D. Varbanetsb a ul. Dvoryanskaya 2, Dept. of computer algebra and discrete mathematics, Odessa national university, Odessa 65026, Ukraine
b ul. Solnechnaya. 7/9 apt.. 18, Odessa. 65009
Ukraine
Abstract:
Let $\tau(\alpha)$ be the number of divisors of the Gaussian integer $\alpha$. An asymptotic formula for the summatory function $\sum\limits_{N(\alpha)\leq x}\tau(\alpha)\tau(\alpha+\beta)$ is obtained under the condition $N(\beta)\leq x^{3/8}$. This is a generalization of the well-known additive divisor problem for the natural numbers.
Keywords:
additive divisor problem; asymptotic formula.
Received: 22.02.2003
Citation:
O. V. Savasrtu, P. D. Varbanets, “An additive divisor problem in $\mathbb{Z}[i]$”, Algebra Discrete Math., 2003, no. 1, 103–110
Linking options:
https://www.mathnet.ru/eng/adm373 https://www.mathnet.ru/eng/adm/y2003/i1/p103
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