New Identities Dealing with Gauss Sums
In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the eight-order and twelve-order characters modulo &l...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/9/1416 |
| _version_ | 1797555569933942784 |
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| author | Wenpeng Zhang Abdul Samad Zhuoyu Chen |
| author_facet | Wenpeng Zhang Abdul Samad Zhuoyu Chen |
| author_sort | Wenpeng Zhang |
| collection | DOAJ |
| description | In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the eight-order and twelve-order characters modulo <i>p</i>, where <i>p</i> be an odd prime with <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>8</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> or <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>12</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T16:49:20Z |
| format | Article |
| id | doaj.art-f67e763c96ba42c5828c9da709214a26 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T16:49:20Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f67e763c96ba42c5828c9da709214a262023-11-20T11:23:20ZengMDPI AGSymmetry2073-89942020-08-01129141610.3390/sym12091416New Identities Dealing with Gauss SumsWenpeng Zhang0Abdul Samad1Zhuoyu Chen2School of Mathematics, Northwest University, Xi’an 710127, Shaanxi, ChinaSchool of Mathematics, Northwest University, Xi’an 710127, Shaanxi, ChinaSchool of Mathematics, Northwest University, Xi’an 710127, Shaanxi, ChinaIn this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the eight-order and twelve-order characters modulo <i>p</i>, where <i>p</i> be an odd prime with <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>8</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> or <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>12</mn><mi>k</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2073-8994/12/9/1416Gauss sumselementary methodidentitycalculating formula |
| spellingShingle | Wenpeng Zhang Abdul Samad Zhuoyu Chen New Identities Dealing with Gauss Sums Symmetry Gauss sums elementary method identity calculating formula |
| title | New Identities Dealing with Gauss Sums |
| title_full | New Identities Dealing with Gauss Sums |
| title_fullStr | New Identities Dealing with Gauss Sums |
| title_full_unstemmed | New Identities Dealing with Gauss Sums |
| title_short | New Identities Dealing with Gauss Sums |
| title_sort | new identities dealing with gauss sums |
| topic | Gauss sums elementary method identity calculating formula |
| url | https://www.mdpi.com/2073-8994/12/9/1416 |
| work_keys_str_mv | AT wenpengzhang newidentitiesdealingwithgausssums AT abdulsamad newidentitiesdealingwithgausssums AT zhuoyuchen newidentitiesdealingwithgausssums |