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The hybrid mean value of Dedekind sums and two-term exponential sums

100%
Leran C., Xiaoxue L.
Open Mathematics
|
2016
|
tom 14
|
nr 1
436-442
EN
In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.
2
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On the Golomb’s conjecture and Lehmer’s numbers

100%
Tingting W., Xiaonan W.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1003-1009
EN
Let p be an odd prime. For each integer a with 1 ≤ a ≤ p − 1, it is clear that there exists one and only one ā with 1 ≤ ā ≤ p − 1 such that a · ā ≡ 1 mod p. Let N(p) denote the set of all primitive roots a mod p with 1 ≤ a ≤ p − 1 in which a and ā are of opposite parity. The main purpose of this paper is using the analytic method and the estimate for the hybrid exponential sums to study the solvability of the congruence a + b ≡ 1 mod p with a, b ∈ N(p), and give a sharper asymptotic formula for the number of the solutions of the congruence equation.
3
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One kind sixth power mean of the three-term exponential sums

100%
Wang X., Li X.
Open Mathematics
|
2017
|
tom 15
|
nr 1
705-710
EN
In this paper, we use the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean of the three-term exponential sums. As a conclusion, we give an exact computational formula for it.
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