A Note on Cube-Full Numbers in Arithmetic Progression
We obtain an asymptotic formula for the cube-full numbers in an arithmetic progression n≡lmod q, where q,l=1. By extending the construction derived from Dirichlet’s hyperbola method and relying on Kloosterman-type exponential sum method, we improve the very recent error term with x118/4029<q....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5552120 |
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| _version_ | 1832554012267773952 |
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| author | Mingxuan Zhong Yuankui Ma |
| author_facet | Mingxuan Zhong Yuankui Ma |
| author_sort | Mingxuan Zhong |
| collection | DOAJ |
| description | We obtain an asymptotic formula for the cube-full numbers in an arithmetic progression n≡lmod q, where q,l=1. By extending the construction derived from Dirichlet’s hyperbola method and relying on Kloosterman-type exponential sum method, we improve the very recent error term with x118/4029<q. |
| format | Article |
| id | doaj-art-584e9ad6be6a474aa02395b10e1d6163 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-584e9ad6be6a474aa02395b10e1d61632025-02-03T05:52:39ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55521205552120A Note on Cube-Full Numbers in Arithmetic ProgressionMingxuan Zhong0Yuankui Ma1School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, Shaanxi, ChinaSchool of Science, Xi’an Technological University, Xi’an 710021, Shaanxi, ChinaWe obtain an asymptotic formula for the cube-full numbers in an arithmetic progression n≡lmod q, where q,l=1. By extending the construction derived from Dirichlet’s hyperbola method and relying on Kloosterman-type exponential sum method, we improve the very recent error term with x118/4029<q.http://dx.doi.org/10.1155/2021/5552120 |
| spellingShingle | Mingxuan Zhong Yuankui Ma A Note on Cube-Full Numbers in Arithmetic Progression Journal of Mathematics |
| title | A Note on Cube-Full Numbers in Arithmetic Progression |
| title_full | A Note on Cube-Full Numbers in Arithmetic Progression |
| title_fullStr | A Note on Cube-Full Numbers in Arithmetic Progression |
| title_full_unstemmed | A Note on Cube-Full Numbers in Arithmetic Progression |
| title_short | A Note on Cube-Full Numbers in Arithmetic Progression |
| title_sort | note on cube full numbers in arithmetic progression |
| url | http://dx.doi.org/10.1155/2021/5552120 |
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