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Some Identities Involving Certain Hardy Sums and General Kloosterman Sums

Author

Listed:
  • Huifang Zhang

    (School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China)

  • Tianping Zhang

    (School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China)

Abstract

Using the properties of Gauss sums, the orthogonality relation of character sum and the mean value of Dirichlet L -function, we obtain some exact computational formulas for the hybrid mean value involving general Kloosterman sums K ( r , l , λ ; p ) and certain Hardy sums S 1 ( h , q ) ∑ m = 1 p − 1 ∑ s = 1 p − 1 K ( m , n , λ ; p ) K ( s , t , λ ; p ) S 1 ( 2 m s ¯ , p ) , ∑ m = 1 p − 1 ∑ s = 1 p − 1 | K ( m , n , λ ; p ) | 2 | K ( s , t , λ ; p ) | 2 S 1 ( 2 m s ¯ , p ) . Our results not only cover the previous results, but also contain something quite new. Actually the previous authors just consider the case of the principal character λ modulo p , while we consider all the cases.

Suggested Citation

  • Huifang Zhang & Tianping Zhang, 2020. "Some Identities Involving Certain Hardy Sums and General Kloosterman Sums," Mathematics, MDPI, vol. 8(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:95-:d:305901
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    References listed on IDEAS

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    1. Maier, Helmut & Rassias, Michael Th., 2019. "Distribution of a cotangent sum related to the Nyman–Beurling criterion for the Riemann Hypothesis," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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