Abstract
The main purpose of this paper is, using the properties of Gauss sums, the estimate for character sums and the analytic method, to study the mean value of the two-term Dedekind sums and give an interesting asymptotic formula for it.
Highlights
Let q be a natural number and h be an integer prime to q
For any odd prime p and integer m with (m, p) =, we consider the mean value of the two-term Dedekind sums p– p
For general integer q >, whether there exists an asymptotic formula for q q a= b= (a,q)= (b,q)=
Summary
1 Introduction Let q be a natural number and h be an integer prime to q. Many authors have studied the arithmetical properties of S(h, q) and obtained many interesting results; see, for example, [ – ] and [ ]. For any odd prime p and integer m with (m, p) = , we consider the mean value of the two-term Dedekind sums p– p–
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