A5101749931- Advanced Mathematical Identities
- Analytic Number Theory Research
- Advanced Mathematical Theories
- Coding theory and cryptography
- Advanced Mathematical Theories and Applications
- Mathematical functions and polynomials
- Advanced Combinatorial Mathematics
- Scientific Research and Discoveries
- Heavy metals in environment
- Heavy Metal Exposure and Toxicity
- Limits and Structures in Graph Theory
- Algebraic Geometry and Number Theory
- Mathematical Inequalities and Applications
- Fractional Differential Equations Solutions
- Water Quality and Pollution Assessment
Xi'an Technological University
2024
State Key Laboratory of Hydraulics and Mountain River Engineering
2021
Northwest University
2017-2021
Sichuan University
2020-2021
Hetao College
2020
Abstract Let p be an odd prime with ≡ 1 mod 4, k any positive integer, ψ fourth-order character . In this paper, we use the analytic method and properties of sums to study computational problem G ( , ) = τ )+ ), give interesting linear recurrence formula for it, where denotes classical Gauss sums.
In this paper, firstly, we introduced a second order non-linear recursive sequence, then use sequence and the combinatorial methods to perform deep study on computational problem concerning one kind sums, which includes Chebyshev polynomials. This makes it possible simplify class of complex computations involving type polynomials into very simple problem. Finally, give new interesting identity for it.
Abstract We apply the analytic method and properties of classical Gauss sums to study computational problem a certain hybrid power mean trigonometric prove several new value formulae for them. At same time, we also obtain recurrence formula involving two-term exponential sums.
The aim of this paper is to use elementary methods and the recursive properties a special sequence study computational problem one kind symmetric sums involving Fubini polynomials Euler numbers, give an interesting formula for it. At same time, we also calculation method general case.
The main aim of this paper is that for any second-order linear recurrence sequence, the generating function which f ( t ) = 1 + a b 2 , we can give exact coefficient expression power series expansion x ∈ R with elementary methods and symmetry properties. On other hand, if take some special values b, not only obtain convolution formula important polynomials, but also establish relationship between polynomials themselves. For example, find Chebyshev Legendre polynomials.
In this article, we used the elementary methods and properties of classical Gauss sums to study problem calculating some sums. particular, obtain interesting formulas for corresponding eight-order twelve-order characters modulo p, where p be an odd prime with p=8k+1 or p=12k+1.
Abstract Studies on trace element (TE) pollution in abiotic matrices have typically focused water, sediment, and soil, either separately or pairs. The importance of multi-media connectivity has been ignored. This study analyzed the concentrations 6 TEs three connected environmental compartments a 28-km section lower reach Jinsha River. ecological risk posed by was higher soil than sediment. contribution exposure pathways to human health were ranked as ingestion > dermal contact...
In this paper, we use the elementary methods, properties of Gauss sums and estimate for character to study calculating problems a certain cubic residues modulo <i>p</i>, give some interesting identities asymptotic formulas their counting functions.
<abstract><p>Our main purpose of this article was using the analytic methods and properties Dirichlet $ L $-functions to study Dedekind sums give a new reciprocity formula for it. As its applications, some exact calculating one kind mean square value $-fuctions with weight character were obtained.</p></abstract>
In this paper, we introduce the fourth-order linear recurrence sequence and its generating function obtain exact coefficient expression of power series expansion using elementary methods symmetric properties summation processes. At same time, establish some relations involving Tetranacci numbers give interesting identities.
The main purpose of this paper is to find explicit expressions for two sequences and solve related conjectures arising from the recent study sums finite products Catalan numbers by Zhang Chen.
Abstract The main purpose of this paper is using the analytic method, properties trigonometric sums and Gauss to study computational problem one kind hybrid power mean involving two different sums, give an interesting formula for it.
The aim of this paper is to use an analytic method and the properties classical Gauss sums research computational problem one kind character sum polynomials modulo odd prime p obtain several meaningful third- fourth-order linear recurrence formulae for them.
The main purpose of this paper is using the analytic methods and properties Legendre's symbol quadratic residue mod <i>p</i> to study computational problem fourth power mean a sum analogous Kloosterman sum, give sharp asymptotic formula for it.
We perform a further investigation for the multiple zeta values and their variations generalizations in this paper. By making use of method generating functions some connections between higher-order trigonometric Lerch function, we explicitly evaluate weighted sums zeta, Hurwitz alternating terms Bernoulli Euler polynomials numbers. It turns out that various known results are deduced as special cases.