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2023, Volume 31, Issue 8: 4579-4591. doi: 10.3934/era.2023234
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The sixth power mean of one kind generalized two-term exponential sums and their asymptotic properties

  • 1.
    School of Information Engineering, Xi'an University, Xi'an, Shaanxi, China
  • 2.
    School of Science, Xi'an Aeronautical Institute, Xi'an, Shaanxi, China
  • Received: 19 January 2023 Revised: 13 June 2023 Accepted: 15 June 2023 Published: 26 June 2023

  • The main aim of this article is using the elementary method and the number of the solutions of some congruence equations modulo an odd prime p, to study the calculating problem of the sixth power mean of one kind generalized two-term exponential sums, and give a sharp asymptotic formula for it.

    Citation: Jin Zhang, Xiaoxue Li. The sixth power mean of one kind generalized two-term exponential sums and their asymptotic properties[J]. Electronic Research Archive, 2023, 31(8): 4579-4591. doi: 10.3934/era.2023234

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  • The main aim of this article is using the elementary method and the number of the solutions of some congruence equations modulo an odd prime p, to study the calculating problem of the sixth power mean of one kind generalized two-term exponential sums, and give a sharp asymptotic formula for it.




    [1] R. Duan, W. P. Zhang, On the fourth power mean of the generalized two-term exponential sums, Math. Rep., 72 (2020), 205–212.
    [2] L. Chen, X. Wang, A new fourth power mean of two-term exponential sums, Open Math., 17 (2019), 407–414. https://doi.org/10.1515/math-2019-0034 doi: 10.1515/math-2019-0034
    [3] W. P. Zhang, H. L. Li, Elementary Number Theory, Shaanxi Normal University Press, Xi'an, 2013.
    [4] W. P. Zhang, Y. Y. Meng, On the sixth power mean of the two-term exponential sums, Acta Math. Sin., Engl. Ser., 38 (2022), 510–518. https://doi.org/10.1007/s10114-022-0541-8 doi: 10.1007/s10114-022-0541-8
    [5] X. Y. Liu, W. P. Zhang, On the high-power mean of the generalized Gauss sums and Kloosterman sums, Mathematics, 7 (2019), 907. https://doi.org/ 10.3390/math7100907 doi: 10.3390/math7100907
    [6] H. Zhang, W. P. Zhang, The fourth power mean of two-term exponential sums and its application, Math. Rep., 69 (2017), 75–81.
    [7] W. P. Zhang, D. Han, On the sixth power mean of the two-term exponential sums, J. Number Theory, 136 (2014), 403–413. http://dx.doi.org/10.1016/j.jnt.2013.10.022 doi: 10.1016/j.jnt.2013.10.022
    [8] H. N. Liu, W. M. Li, On the fourth power mean of the three-term exponential sums, Adv. Math., 46 (2017), 529–547.
    [9] X. C. Du, X. X. Li, On the fourth power mean of generalized three-term exponential sums, J. Math. Res. Appl., 35 (2015), 92–96.
    [10] X. Y. Wang, X. X. Li, One kind sixth power mean of the three-term exponential sums, Open Math., 15 (2017), 705–710. http://dx.doi.org/10.1515/math-2017-0060 doi: 10.1515/math-2017-0060
    [11] T. M. Apostol, SIntroduction to Analytic Number Theory, Springer-Verlag, New York, 1976. https://doi.org/10.1007/978-1-4757-5579-4
    [12] K. Ireland, M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1982. https://doi.org/10.1007/978-1-4757-1779-2

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