On the fourth-order linear recurrence formula related to classical Gauss sums
Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ), and give an interesting fourth-order linear recu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-10-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2017-0104 |
| _version_ | 1819122060328173568 |
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| author | Zhuoyu Chen Wenpeng Zhang |
| author_facet | Zhuoyu Chen Wenpeng Zhang |
| author_sort | Zhuoyu Chen |
| collection | DOAJ |
| description | Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ), and give an interesting fourth-order linear recurrence formula for it, where τ(ψ) denotes the classical Gauss sums. |
| first_indexed | 2024-12-22T06:46:27Z |
| format | Article |
| id | doaj.art-8954f7ae706346129d298003fd0f350f |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-22T06:46:27Z |
| publishDate | 2017-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-8954f7ae706346129d298003fd0f350f2022-12-21T18:35:17ZengDe GruyterOpen Mathematics2391-54552017-10-011511251125510.1515/math-2017-0104math-2017-0104On the fourth-order linear recurrence formula related to classical Gauss sumsZhuoyu Chen0Wenpeng Zhang1School of Mathematics, Northwest University, Xi’an, Shaanxi, ChinaSchool of Mathematics, Northwest University, Xi’an, Shaanxi, ChinaLet p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ), and give an interesting fourth-order linear recurrence formula for it, where τ(ψ) denotes the classical Gauss sums.https://doi.org/10.1515/math-2017-0104the classical gauss sumsfourth-order linear recurrence formulaanalytic methodcharacter sums11l0511l0711t24 |
| spellingShingle | Zhuoyu Chen Wenpeng Zhang On the fourth-order linear recurrence formula related to classical Gauss sums Open Mathematics the classical gauss sums fourth-order linear recurrence formula analytic method character sums 11l05 11l07 11t24 |
| title | On the fourth-order linear recurrence formula related to classical Gauss sums |
| title_full | On the fourth-order linear recurrence formula related to classical Gauss sums |
| title_fullStr | On the fourth-order linear recurrence formula related to classical Gauss sums |
| title_full_unstemmed | On the fourth-order linear recurrence formula related to classical Gauss sums |
| title_short | On the fourth-order linear recurrence formula related to classical Gauss sums |
| title_sort | on the fourth order linear recurrence formula related to classical gauss sums |
| topic | the classical gauss sums fourth-order linear recurrence formula analytic method character sums 11l05 11l07 11t24 |
| url | https://doi.org/10.1515/math-2017-0104 |
| work_keys_str_mv | AT zhuoyuchen onthefourthorderlinearrecurrenceformularelatedtoclassicalgausssums AT wenpengzhang onthefourthorderlinearrecurrenceformularelatedtoclassicalgausssums |