On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums
The main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some interesting fourth-order linear recurrence formula...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-08-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2018-0081 |
| _version_ | 1818865960852914176 |
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| author | Shen Shimeng |
| author_facet | Shen Shimeng |
| author_sort | Shen Shimeng |
| collection | DOAJ |
| description | The main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some interesting fourth-order linear recurrence formulae for this problem. As an application of our result, we can also obtain an exact computational formula for one kind congruence equation mod p, an odd prime. |
| first_indexed | 2024-12-19T10:55:51Z |
| format | Article |
| id | doaj.art-d6a78cfa923f4e5683e348afdc176017 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-19T10:55:51Z |
| publishDate | 2018-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-d6a78cfa923f4e5683e348afdc1760172022-12-21T20:24:49ZengDe GruyterOpen Mathematics2391-54552018-08-0116195596610.1515/math-2018-0081math-2018-0081On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sumsShen Shimeng0School of Mathematics, Northwest University, Xi’an, Shaanxi, ChinaThe main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some interesting fourth-order linear recurrence formulae for this problem. As an application of our result, we can also obtain an exact computational formula for one kind congruence equation mod p, an odd prime.https://doi.org/10.1515/math-2018-0081the quartic gauss sumstwo-term exponential sumshybrid power meanthe fourth-order linear recurrence formula11l0511l07 |
| spellingShingle | Shen Shimeng On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums Open Mathematics the quartic gauss sums two-term exponential sums hybrid power mean the fourth-order linear recurrence formula 11l05 11l07 |
| title | On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums |
| title_full | On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums |
| title_fullStr | On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums |
| title_full_unstemmed | On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums |
| title_short | On the recursive properties of one kind hybrid power mean involving two-term exponential sums and Gauss sums |
| title_sort | on the recursive properties of one kind hybrid power mean involving two term exponential sums and gauss sums |
| topic | the quartic gauss sums two-term exponential sums hybrid power mean the fourth-order linear recurrence formula 11l05 11l07 |
| url | https://doi.org/10.1515/math-2018-0081 |
| work_keys_str_mv | AT shenshimeng ontherecursivepropertiesofonekindhybridpowermeaninvolvingtwotermexponentialsumsandgausssums |