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A Note on the Sixth Power Mean Value of the Generalized Quadratic Gauss Sums

Authors:

XiaoChuan Ai,

XiangKun JiAuthors Info & Claims

ICVISP 2019: Proceedings of the 3rd International Conference on Vision, Image and Signal Processing

Article No.: 71, Pages 1 - 6

https://doi.org/10.1145/3387168.3387251

Published: 25 May 2020 Publication History

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Abstract

In In this paper, the sixth mean value of the generalized quadratic Gauss sums considered by Y.F. He and W.P. Zhang is further studied when module is an arbitrary square-full number. The precise calculation formula is obtained. This improves the existed research result by averting the restriction that the module being an odd square-full number.

References

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A.Weil On some exponential sums(1948). Proc. Nat. Acad. Sci. U.S.A., 34: 203--210.

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Cochrane, Z.Y. Zheng(1999). Pure and mixed exponential sums. Acta Arith., 91:249--278.

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[3]

L. K. Hua.1979. Introduction to number theory(1st. ed.). Science Press. Beijing, China, Chapter 7.

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[4]

W.P. Zhang(2002). Moments of Generalized Quadratic Gauss Sums Weighted by L-Functions. J. Number Theory, 92: 304--314.

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W.P. Zhang, Y.P. Deng(2002). A hybrid mean value of the inversion of L-functions and general Quadratic Gauss sums. Nagoya Math. J., 167: 1--15.

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[6]

W.P. Zhang, H.L.Liu(2005). On the general Gauss sums and their fourth power mean. Osaka J. Math., 42(1): 189--199.

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[7]

Y.F. He, W.P. Zhang(2011). On the 2k-th power mean value of the generalized quadratic Guass sums. Bull. Korean Math.Soc., 48(1): 9--15.

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Index Terms

A Note on the Sixth Power Mean Value of the Generalized Quadratic Gauss Sums
1. Theory of computation
  1. Logic
    1. Proof theory

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ICVISP 2019: Proceedings of the 3rd International Conference on Vision, Image and Signal Processing

August 2019

584 pages

ISBN:9781450376259

DOI:10.1145/3387168

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Association for Computing Machinery

New York, NY, United States

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Published: 25 May 2020

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ICVISP 2019

ICVISP 2019: 3rd International Conference on Vision, Image and Signal Processing

August 26 - 28, 2019

BC, Vancouver, Canada

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ICVISP 2019 Paper Acceptance Rate 126 of 277 submissions, 45%;

Overall Acceptance Rate 186 of 424 submissions, 44%

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A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials

On Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae

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A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials

On Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae

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