Abstract
The main purpose of this paper is using the properties of Gauss sums and the mean value theorem of the Dirichlet L-functions to study one kind of a hybrid mean value problem involving certain Hardy sums and Ramanujan’s sum and to give an exact computational formula for it.MSC:11L05, 11L10.
Highlights
Let c be a natural number and d be an integer prime to c
The main purpose of this paper is using the properties of Gauss sums and the mean square value theorem of the Dirichlet L-functions to study a hybrid mean value problem involving certain Hardy sums and Ramanujan’s sum and to give an exact computational formula for it
Authors’ contributions WW carried out the hybrid mean value problem involving certain Hardy sums and Ramanujan’s sum and gave an exact computational formula
Summary
Let c be a natural number and d be an integer prime to c. Regarding the properties of S (d, c) and related sums, some authors studied them and obtained many interesting results; see [ – ] and [ ]. The main purpose of this paper is using the properties of Gauss sums and the mean square value theorem of the Dirichlet L-functions to study a hybrid mean value problem involving certain Hardy sums and Ramanujan’s sum and to give an exact computational formula for it. Theorem Let q > be an odd square-full number.
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