Research article

A certain new Gauss sum and its fourth power mean

  • Received: 13 April 2020 Accepted: 01 June 2020 Published: 09 June 2020
  • MSC : 11L03, 11L07

  • The main purpose of this paper is using the elementary methods and the properties of the Legendre symbol to study the computational problem of the fourth power mean of a certain generalized quadratic Gauss sum, and give two exact calculating formulae for it.

    Citation: Yan Zhao, Wenpeng Zhang, Xingxing Lv. A certain new Gauss sum and its fourth power mean[J]. AIMS Mathematics, 2020, 5(5): 5004-5011. doi: 10.3934/math.2020321

    Related Papers:

  • The main purpose of this paper is using the elementary methods and the properties of the Legendre symbol to study the computational problem of the fourth power mean of a certain generalized quadratic Gauss sum, and give two exact calculating formulae for it.


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    [3] W. P. Zhang, X. Lin, On the fourth power mean of the generalized quadratic Gauss sums, Acta Math. Sin., 34 (2018), 1037-1049. doi: 10.1007/s10114-017-7188-x
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    [9] H. Di, A Hybrid mean value involving two-term exponential sums and polynomial character sums, Czech. Math. J., 64 (2014), 53-62. doi: 10.1007/s10587-014-0082-0
    [10] W. P. Zhang, On the fourth and sixth power mean of the classical Kloosterman sums, J. Number Theory, 131 (2011), 228-238. doi: 10.1016/j.jnt.2010.08.008
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    [12] W. P. Zhang, On the fourth power mean of the general Kloosterman sums, J. Number Theory, 169 (2016), 315-326. doi: 10.1016/j.jnt.2016.05.018
    [13] W. P. Zhang, S. M. Shen, A note on the fourth power mean of the generalized Kloosterman sums, J. Number Theory, 174 (2017), 419-426. doi: 10.1016/j.jnt.2016.11.020
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  • © 2020 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)
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