On the high-th mean of one special character sums modulo a prime
Using the elementary method of the classical Gauss sums and the properties of character sums, we study a linear recurrence formula about the form $ G\left(n\right) = 1+\sum_{a = 1}^{p-1}\left(\frac{a^2+n\bar{a}^2}{p}\right) $ and about the mean value of $ G(n) $. This is a further exploration of Yua...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231316?viewType=HTML |
| _version_ | 1797674377303556096 |
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| author | Yan Ma Di Han |
| author_facet | Yan Ma Di Han |
| author_sort | Yan Ma |
| collection | DOAJ |
| description | Using the elementary method of the classical Gauss sums and the properties of character sums, we study a linear recurrence formula about the form $ G\left(n\right) = 1+\sum_{a = 1}^{p-1}\left(\frac{a^2+n\bar{a}^2}{p}\right) $ and about the mean value of $ G(n) $. This is a further exploration of Yuan and Zhang's research in 2022, which help us to better understand the character sums wide range application. |
| first_indexed | 2024-03-11T21:58:10Z |
| format | Article |
| id | doaj.art-f088d9a741314351a7f50c33e974169d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T21:58:10Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-f088d9a741314351a7f50c33e974169d2023-09-26T01:30:45ZengAIMS PressAIMS Mathematics2473-69882023-09-01811258042581410.3934/math.20231316On the high-th mean of one special character sums modulo a primeYan Ma0Di Han1Research Center for Number Theory and Its Applications, Northwest University, Xi'an 710127, ChinaResearch Center for Number Theory and Its Applications, Northwest University, Xi'an 710127, ChinaUsing the elementary method of the classical Gauss sums and the properties of character sums, we study a linear recurrence formula about the form $ G\left(n\right) = 1+\sum_{a = 1}^{p-1}\left(\frac{a^2+n\bar{a}^2}{p}\right) $ and about the mean value of $ G(n) $. This is a further exploration of Yuan and Zhang's research in 2022, which help us to better understand the character sums wide range application.https://www.aimspress.com/article/doi/10.3934/math.20231316?viewType=HTMLquadratic characterquartic characterbasic methodcalculating formulaspecial character sums |
| spellingShingle | Yan Ma Di Han On the high-th mean of one special character sums modulo a prime AIMS Mathematics quadratic character quartic character basic method calculating formula special character sums |
| title | On the high-th mean of one special character sums modulo a prime |
| title_full | On the high-th mean of one special character sums modulo a prime |
| title_fullStr | On the high-th mean of one special character sums modulo a prime |
| title_full_unstemmed | On the high-th mean of one special character sums modulo a prime |
| title_short | On the high-th mean of one special character sums modulo a prime |
| title_sort | on the high th mean of one special character sums modulo a prime |
| topic | quadratic character quartic character basic method calculating formula special character sums |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231316?viewType=HTML |
| work_keys_str_mv | AT yanma onthehighthmeanofonespecialcharactersumsmoduloaprime AT dihan onthehighthmeanofonespecialcharactersumsmoduloaprime |