Evaluations of a Weighted Average of Gauss Sums
In this paper, we perform a further investigation for a weighted average of Gauss sums. By making use of some properties of the cotangent function and the Bernoulli polynomials, we explicitly evaluate the weighted average of Gauss sums in terms of the special values of Dirichlet L-functions at posit...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6206329 |
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| _version_ | 1832566445370769408 |
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| author | Wen-Kai Shao Yuan He |
| author_facet | Wen-Kai Shao Yuan He |
| author_sort | Wen-Kai Shao |
| collection | DOAJ |
| description | In this paper, we perform a further investigation for a weighted average of Gauss sums. By making use of some properties of the cotangent function and the Bernoulli polynomials, we explicitly evaluate the weighted average of Gauss sums in terms of the special values of Dirichlet L-functions at positive integers. |
| format | Article |
| id | doaj-art-e1f89b6ed4bd47158007b445eb3f0e66 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e1f89b6ed4bd47158007b445eb3f0e662025-02-03T01:04:10ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/62063296206329Evaluations of a Weighted Average of Gauss SumsWen-Kai Shao0Yuan He1Department of Mathematical Teaching and Research, Yibin Vocational & Technical College, Yibin 644003, Sichuan, ChinaSchool of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, Sichuan, ChinaIn this paper, we perform a further investigation for a weighted average of Gauss sums. By making use of some properties of the cotangent function and the Bernoulli polynomials, we explicitly evaluate the weighted average of Gauss sums in terms of the special values of Dirichlet L-functions at positive integers.http://dx.doi.org/10.1155/2021/6206329 |
| spellingShingle | Wen-Kai Shao Yuan He Evaluations of a Weighted Average of Gauss Sums Journal of Mathematics |
| title | Evaluations of a Weighted Average of Gauss Sums |
| title_full | Evaluations of a Weighted Average of Gauss Sums |
| title_fullStr | Evaluations of a Weighted Average of Gauss Sums |
| title_full_unstemmed | Evaluations of a Weighted Average of Gauss Sums |
| title_short | Evaluations of a Weighted Average of Gauss Sums |
| title_sort | evaluations of a weighted average of gauss sums |
| url | http://dx.doi.org/10.1155/2021/6206329 |
| work_keys_str_mv | AT wenkaishao evaluationsofaweightedaverageofgausssums AT yuanhe evaluationsofaweightedaverageofgausssums |