### AIMS Mathematics

2021, Issue 2: 1596-1606. doi: 10.3934/math.2021095
Research article

# New identities involving Hardy sums $S_3(h, k)$ and general Kloosterman sums

• Received: 26 May 2020 Accepted: 23 November 2020 Published: 25 November 2020
• MSC : 11F20, 11L05

• The main purpose of this paper is to obtain some exact computational formulas or upper bounds for hybrid mean value involving Hardy sums $S_{3}(h, p)$ and general Kloosterman sums $K(r, l, \lambda; p)$. By applying the properties of Gauss sums and the mean value theorems of Dirichlet $L$-function, we derive some new identities. As the special cases, we also deduce some exact computational formulas for hybrid mean value involving $S_{3}(h, p)$ and classical Kloosterman sums $K(n, p)$.

Citation: Wenjia Guo, Yuankui Ma, Tianping Zhang. New identities involving Hardy sums $S_3(h, k)$ and general Kloosterman sums[J]. AIMS Mathematics, 2021, 6(2): 1596-1606. doi: 10.3934/math.2021095

### Related Papers:

• The main purpose of this paper is to obtain some exact computational formulas or upper bounds for hybrid mean value involving Hardy sums $S_{3}(h, p)$ and general Kloosterman sums $K(r, l, \lambda; p)$. By applying the properties of Gauss sums and the mean value theorems of Dirichlet $L$-function, we derive some new identities. As the special cases, we also deduce some exact computational formulas for hybrid mean value involving $S_{3}(h, p)$ and classical Kloosterman sums $K(n, p)$.

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