An additive divisor problem in \(\mathbb{Z}[i]\)

• Дата: 2018
• Автори: Savasrtu, O. V., Varbanets, P. D.
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2018
• Теми: additive divisor problem; asymptotic formula; 11N37; 11R42
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1146
• Назва журналу: Algebra and Discrete Mathematics

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 add...