Results 1 to 10 of about 193 (46)
An Algorithm for the explicit evaluation of GL(n, R) Kolsterman sums [PDF]
, 2009 An algorithm for the explicit evaluation of Kloosterman sums for GL(n, R) for n ≥2 and an implementation in the Mathematics package GL(n) pack are ...
Broughan, Kevin A.
core +2 more sources
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
doaj +1 more source
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
wiley +1 more source
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
doaj +1 more source
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
doaj +1 more source
An improvement on Olson's constant for Zp(+)Zp [PDF]
, 2010 A
Bhowmik, Gautami +1 more
core +3 more sources
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
doaj +1 more source
Restricted linear congruences [PDF]
, 2016 In this paper, using properties of Ramanujan sums and of the discrete Fourier transform of arithmetic functions, we give an explicit formula for the number of solutions of the linear congruence $a_1x_1+\cdots +a_kx_k\equiv b \pmod{n}$, with $\gcd(x_i,n ...
Bibak, Khodakhast +4 more
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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 number of solutions of a restricted linear congruence
, 2017 Consider the linear congruence equation $${a_1^{s}x_1+\ldots+a_k^{s} x_k \equiv b\,(\text{mod } n^s)}\text { where } a_i,b\in\mathbb{Z},s\in\mathbb{N}$$ Denote by $(a,b)_s$ the largest $l^s\in\mathbb{N}$ which divides $a$ and $b$ simultaneously.
Namboothiri, K Vishnu
core +1 more source