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Some Identities Involving Certain Hardy Sums and General Kloosterman Sums

School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China
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Mathematics 2020, 8(1), 95; https://doi.org/10.3390/math8010095
Received: 20 November 2019 / Revised: 2 January 2020 / Accepted: 2 January 2020 / Published: 7 January 2020
(This article belongs to the Special Issue Special Polynomials)
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. View Full-Text
Keywords: certain Hardy sums; general Kloosterman sums; hybrid mean value; exact computational formulas certain Hardy sums; general Kloosterman sums; hybrid mean value; exact computational formulas
MDPI and ACS Style

Zhang, H.; Zhang, T. Some Identities Involving Certain Hardy Sums and General Kloosterman Sums. Mathematics 2020, 8, 95.

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