Bulletin of the
Korean Mathematical Society BKMS

The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that $q$ is a prime.

Keywords: Hybrid mean value, Kloosterman sums, generalized Dedekind sums, generalized Hardy sums

MSC numbers: Primary 11F20, 11L05

Supported by: This work is supported by the Natural Science Basic Research Plan in Shaanxi Province of China (NO.2021JQ-495) and the National Natural Science Foundation of China (NO.61902304).