Results 1 to 10 of about 15 (15)
The hybrid mean value of Dedekind sums and two-term exponential sums
Open Mathematics, 2016 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 ...
Leran Chang, Xiaoxue Li
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On the existence of a non‐zero lower bound for the number of Goldbach partitions of an even integer
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 15, Page 789-798, 2004., 2004 The Goldbach partitions of an even number, given by the sums of two prime addends, form the nonempty set for all integers 2n with 2 ≤ n ≤ 2 × 1014. It will be shown how to determine by the method of induction the existence of a non‐zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4.
Simon Davis
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One kind power mean of the hybrid Gauss sums
Open Mathematics, 2018 In this paper, we use the analysis method and the properties of trigonometric sums to study the computational problem of one kind power mean of the hybrid Gauss sums. After establishing some relevant lemmas, we give an exact computational formula for it.
Lan Qi, Wenpeng Zhang
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On the two-term exponential sums and character sums of polynomials
Open Mathematics, 2019 The main aim of this paper is to use the analytic methods and the properties of the classical Gauss sums to research the computational problem of one kind hybrid power mean containing the character sums of polynomials and two-term exponential sums modulo
Ma Yuankui, Zhang Wenpeng
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One kind sixth power mean of the three-term exponential sums
Open Mathematics, 2017 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.
Wang Xiaoying, Li Xiaoxue
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On the Golomb’s conjecture and Lehmer’s numbers
Open Mathematics, 2017 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
Tingting Wang, Xiaonan Wang
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On the generalized exponential sums and their fourth power mean
Open MathematicsThe main purpose of this article is to study the calculating problem of the fourth power mean of the two-term exponential sums and provide an accurate calculating formula for utilizing analytical methods and character sums’ properties. In the meantime, a
Liu Wencong, Ning Shushu
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Journal of Mathematics, Volume 2024, Issue 1, 2024.The primary contribution of this paper is to research one kind special Kloosterman sums using analytic method. We translate one kind fourth power mean of the Kloosterman sums into the character sums of one kind polynomials. It is possible to construct an exact formula for the fourth power mean of one kind Kloosterman sums by computing the character ...
Shushu Ning, Xuexia Wang, Ming-Sheng Liu
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A study on two types of degenerate unipoly-Dedekind sums
Applied Mathematics in Science and EngineeringIn this paper, we study the degenerate unipoly-Dedekind sums rising from the type 2 degenerate unipoly Bernoulli functions and degenerate unipoly-Bernoulli functions of arbitrary indices, respectively.
Wencong Liu +3 more
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One special kind of Kloosterman sum and its fourth-power mean
Open MathematicsThis article aims to investigate the calculation problem of the fourth-power mean of the specific Kloosterman sums by utilizing analytic methods and the properties of classical Gauss sums.
Zhang Wenpeng, Wang Li, Liu Xiaoge
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