The Kloosterman sums on the ellipse
The main point of our research is to obtain the estimates for Kloosterman sums \(\widetilde{K}(\alpha,\beta;h,q;k)\) considered on the ellipse bound for the case of the integer rational module \(q\) and for some natural number \(k\) with conditions \((\alpha,q)=(\beta,q)=1\) on the integer numbers o...
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| Date: | 2023 |
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Lugansk National Taras Shevchenko University
2023
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admjournalluguniveduua-article-20482023-10-30T03:23:55Z The Kloosterman sums on the ellipse Varbanets, S. Vorobyov, Y. exponential sums, Kloosterman sums, asymptotic formulas, imaginary quadratic field 11L05, 11L07, 11T23 The main point of our research is to obtain the estimates for Kloosterman sums \(\widetilde{K}(\alpha,\beta;h,q;k)\) considered on the ellipse bound for the case of the integer rational module \(q\) and for some natural number \(k\) with conditions \((\alpha,q)=(\beta,q)=1\) on the integer numbers of imaginary quadratic field. These estimates can be used to construct the asymptotic formulas for the sum of divisors function \(\tau_\ell(\alpha)\) for \(\ell=2,3,\ldots\) over the ring of integer elements of imaginary quadratic field in arithmetic progression. Lugansk National Taras Shevchenko University 2023-10-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2048 10.12958/adm2048 Algebra and Discrete Mathematics; Vol 35, No 2 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2048/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2048/1033 Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2023-10-30T03:23:55Z |
| collection |
OJS |
| language |
English |
| topic |
exponential sums Kloosterman sums asymptotic formulas imaginary quadratic field 11L05 11L07 11T23 |
| spellingShingle |
exponential sums Kloosterman sums asymptotic formulas imaginary quadratic field 11L05 11L07 11T23 Varbanets, S. Vorobyov, Y. The Kloosterman sums on the ellipse |
| topic_facet |
exponential sums Kloosterman sums asymptotic formulas imaginary quadratic field 11L05 11L07 11T23 |
| format |
Article |
| author |
Varbanets, S. Vorobyov, Y. |
| author_facet |
Varbanets, S. Vorobyov, Y. |
| author_sort |
Varbanets, S. |
| title |
The Kloosterman sums on the ellipse |
| title_short |
The Kloosterman sums on the ellipse |
| title_full |
The Kloosterman sums on the ellipse |
| title_fullStr |
The Kloosterman sums on the ellipse |
| title_full_unstemmed |
The Kloosterman sums on the ellipse |
| title_sort |
kloosterman sums on the ellipse |
| description |
The main point of our research is to obtain the estimates for Kloosterman sums \(\widetilde{K}(\alpha,\beta;h,q;k)\) considered on the ellipse bound for the case of the integer rational module \(q\) and for some natural number \(k\) with conditions \((\alpha,q)=(\beta,q)=1\) on the integer numbers of imaginary quadratic field. These estimates can be used to construct the asymptotic formulas for the sum of divisors function \(\tau_\ell(\alpha)\) for \(\ell=2,3,\ldots\) over the ring of integer elements of imaginary quadratic field in arithmetic progression. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2048 |
| work_keys_str_mv |
AT varbanetss thekloostermansumsontheellipse AT vorobyovy thekloostermansumsontheellipse AT varbanetss kloostermansumsontheellipse AT vorobyovy kloostermansumsontheellipse |
| first_indexed |
2025-12-02T15:35:24Z |
| last_indexed |
2025-12-02T15:35:24Z |
| _version_ |
1850411292705161216 |