An additive divisor problem in \(\mathbb{Z}[i]\)
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...
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| Datum: | 2018 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1146 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-11462018-05-13T06:43:21Z An additive divisor problem in \(\mathbb{Z}[i]\) Savasrtu, O. V. Varbanets, P. D. additive divisor problem, asymptotic formula 11N37, 11R42 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. Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1146 Algebra and Discrete Mathematics; Vol 2, No 1 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1146/638 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-05-13T06:43:21Z |
| collection |
OJS |
| language |
English |
| topic |
additive divisor problem asymptotic formula 11N37 11R42 |
| spellingShingle |
additive divisor problem asymptotic formula 11N37 11R42 Savasrtu, O. V. Varbanets, P. D. An additive divisor problem in \(\mathbb{Z}[i]\) |
| topic_facet |
additive divisor problem asymptotic formula 11N37 11R42 |
| format |
Article |
| author |
Savasrtu, O. V. Varbanets, P. D. |
| author_facet |
Savasrtu, O. V. Varbanets, P. D. |
| author_sort |
Savasrtu, O. V. |
| title |
An additive divisor problem in \(\mathbb{Z}[i]\) |
| title_short |
An additive divisor problem in \(\mathbb{Z}[i]\) |
| title_full |
An additive divisor problem in \(\mathbb{Z}[i]\) |
| title_fullStr |
An additive divisor problem in \(\mathbb{Z}[i]\) |
| title_full_unstemmed |
An additive divisor problem in \(\mathbb{Z}[i]\) |
| title_sort |
additive divisor problem in \(\mathbb{z}[i]\) |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1146 |
| work_keys_str_mv |
AT savasrtuov anadditivedivisorprobleminmathbbzi AT varbanetspd anadditivedivisorprobleminmathbbzi AT savasrtuov additivedivisorprobleminmathbbzi AT varbanetspd additivedivisorprobleminmathbbzi |
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2025-12-02T15:41:56Z |
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2025-12-02T15:41:56Z |
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1850411703527800832 |