Abstract
The main purpose of this paper is using analytic methods and the properties of the Dedekind sums to study one kind hybrid power mean calculating problem involving the Dedekind sums and cubic Gauss sum and give some interesting calculating formulae for it.
Highlights
For any integer q ≥ 3 and integer m, the classical cubic Gauss sum A(m, q) is defined as follows: q− 1 ma3A(m, q) e , (1)a 0 q where as usual, e(x) e2πix and i2 − 1.is sum plays a very important role in the study of the elementary number theory and analytic number theory, so there are many people who had studied the arithmetical properties of A(m, q) and related contents
Is sum plays a very important role in the study of the elementary number theory and analytic number theory, so there are many people who had studied the arithmetical properties of A(m, q) and related contents
E main purpose of this paper is using the analytic method and the properties of Dedekind sums to study the computational problem of the hybrid power mean: Journal of Mathematics
Summary
For any integer q ≥ 3 and integer m, the classical cubic Gauss sum A(m, q) is defined as follows: q− 1 ma. We define the Dedekind sums S(h, q) as follows. Let q be a natural number and h be an integer prime to q. E classical Dedekind sum S(h, q) is defined as qa ah. E main purpose of this paper is using the analytic method and the properties of Dedekind sums to study the computational problem of the hybrid power mean: Journal of Mathematics. Give some exact computational formulae for (5) with q p, an odd prime, where h and k are any two fixed positive integers. En, for any positive integer k, we have the asymptotic formula as follows: S2(m, p) Ak(m, p).
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