Research article Special Issues

One kind two-term exponential sums weighted by third-order character

  • Received: 05 January 2024 Revised: 18 February 2024 Accepted: 23 February 2024 Published: 08 March 2024
  • MSC : 11L03, 11L05

  • We give a correction to the previous paper of S. F. Cao and T. T. Wang (2021). Additionally, provide a conversion formula of the power mean of a certain exponential sums weighted by a Dirichlet character $ \chi_{3} $ and some of its applications.

    Citation: Guohui Chen, Wenpeng Zhang. One kind two-term exponential sums weighted by third-order character[J]. AIMS Mathematics, 2024, 9(4): 9597-9607. doi: 10.3934/math.2024469

    Related Papers:

  • We give a correction to the previous paper of S. F. Cao and T. T. Wang (2021). Additionally, provide a conversion formula of the power mean of a certain exponential sums weighted by a Dirichlet character $ \chi_{3} $ and some of its applications.



    加载中


    [1] T. M. Apostol, Introduction to Analytic Number Theory, New York: Springer-Verlag, 1976.
    [2] S. F. Cao, T. T. Wang, On the hybrid power mean of two-term exponential sums and cubic Gauss sums, J. Math., 8 (2021), 6638156. https://doi.org/10.1155/2021/6638156 doi: 10.1155/2021/6638156
    [3] R. Duan, W. P. Zhang, On the fourth power mean of the generalized two-term exponential sums, Math. Rep., 22 (2020), 205–212.
    [4] J. Greene, D. Stanton, The triplication formula for Gauss sums, Aequat. Math., 30 (1986), 143–141. https://doi.org/10.1007/BF02189920 doi: 10.1007/BF02189920
    [5] X. X. Li, Z. F. Xu, The fourth power mean of the generalized two-term exponential sums and its upper and lower bound estimates, J. Inequal. Appl., 2013 (2013), 504. https://doi.org/10.1186/1029-242X-2013-504 doi: 10.1186/1029-242X-2013-504
    [6] T. T. Wang, W. P. Zhang, On the eighth power mean of the two-term exponential sums, Finite Fields Appl., 92 (2023), 102285. https://doi.org/10.1016/j.ffa.2023.102285 doi: 10.1016/j.ffa.2023.102285
    [7] X. X. Wang, L. Wang, A new two-term exponential sums and its fourth power mean, Rendiconti Circolo Mate. Palermo, 8 (2023), 4041–4052. https://doi.org/10.1007/s12215-023-00879-3 doi: 10.1007/s12215-023-00879-3
    [8] J. M. Yu, R. J. Yuan, T. T. Wang, The fourth power mean value of one kind two-term exponential sums, AIMS Math., 9 (2022), 17045–17060. https://doi.org/10.3934/math.2022937 doi: 10.3934/math.2022937
    [9] H. Zhang, W. P. Zhang, The fourth power mean of two-term exponential sums and its application, Math. Rep. (Bucureşti), 96 (2017), 75–83.
    [10] J. Zhang, W. P. Zhang, A certain two-term exponential sum and its fourth power means, AIMS Math., 6 (2020), 7500–7509. https://doi.org/10.3934/math.2020480 doi: 10.3934/math.2020480
    [11] W. P. Zhang, Moments of generalized quadratic Gauss sums weighted by $L$-functions, J. Number Theory, 2 (2002), 304–314. https://doi.org/10.1006/jnth.2001.2715 doi: 10.1006/jnth.2001.2715
    [12] W. P. Zhang, D. Han, On the sixth power mean of the two-term exponential sums, J. Number Theory, 136 (2014), 403–413. https://doi.org/10.1016/j.jnt.2013.10.022 doi: 10.1016/j.jnt.2013.10.022
    [13] W. P. Zhang, J. Y. Hu, The number of solutions of the diagonal cubic congruence equation $\bmod p$, Math. Rep., 20 (2018), 73–80.
    [14] W. P. Zhang, H. L. Li, Elementary Number Theory, Xi'an: Shaanxi Normal University Press, 2013.
    [15] W. P. Zhang, Y. Y. Meng, On the fourth power mean of one special two-term exponential sums, AIMS Math., 4 (2023), 8650–8660. https://doi.org/10.3934/math.2023434 doi: 10.3934/math.2023434
    [16] W. P. Zhang, Y. Y. Meng, On the sixth power mean of one kind two-term exponential sums weighted by Legendre's symbol modulo $p$, AIMS Math., 7 (2021), 6961–6974. https://doi.org/10.3934/math.2021408 doi: 10.3934/math.2021408
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(550) PDF downloads(86) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog