On the generalized Cochrane sum with Dirichlet characters
In this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231542?viewType=HTML |
| _version_ | 1797508480007929856 |
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| author | Jiankang Wang Zhefeng Xu Minmin Jia |
| author_facet | Jiankang Wang Zhefeng Xu Minmin Jia |
| author_sort | Jiankang Wang |
| collection | DOAJ |
| description | In this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters and obtained a sharp asymptotic formula for it. By using this asymptotic formula, we also gave the mean value of the generalized Dedekind sum. |
| first_indexed | 2024-03-10T05:04:35Z |
| format | Article |
| id | doaj.art-e2c6b3bd72f349429c645e4cab984835 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-10T05:04:35Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-e2c6b3bd72f349429c645e4cab9848352023-11-23T01:27:27ZengAIMS PressAIMS Mathematics2473-69882023-11-01812301823019310.3934/math.20231542On the generalized Cochrane sum with Dirichlet charactersJiankang Wang0Zhefeng Xu1Minmin Jia2Research 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, ChinaResearch Center for Number Theory and Its Applications, Northwest University, Xi'an 710127, ChinaIn this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters and obtained a sharp asymptotic formula for it. By using this asymptotic formula, we also gave the mean value of the generalized Dedekind sum.https://www.aimspress.com/article/doi/10.3934/math.20231542?viewType=HTMLgeneralized cochrane sumdirichlet characterupper boundmean value |
| spellingShingle | Jiankang Wang Zhefeng Xu Minmin Jia On the generalized Cochrane sum with Dirichlet characters AIMS Mathematics generalized cochrane sum dirichlet character upper bound mean value |
| title | On the generalized Cochrane sum with Dirichlet characters |
| title_full | On the generalized Cochrane sum with Dirichlet characters |
| title_fullStr | On the generalized Cochrane sum with Dirichlet characters |
| title_full_unstemmed | On the generalized Cochrane sum with Dirichlet characters |
| title_short | On the generalized Cochrane sum with Dirichlet characters |
| title_sort | on the generalized cochrane sum with dirichlet characters |
| topic | generalized cochrane sum dirichlet character upper bound mean value |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231542?viewType=HTML |
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