A5087263253- Analytic Number Theory Research
- Coding theory and cryptography
- Algebraic Geometry and Number Theory
- Advanced Mathematical Identities
- Finite Group Theory Research
- graph theory and CDMA systems
- Advanced Combinatorial Mathematics
- Mathematics and Applications
- Advanced Algebra and Geometry
- History and Theory of Mathematics
- Soil Mechanics and Vehicle Dynamics
- Advanced Mathematical Theories and Applications
- Agricultural Engineering and Mechanization
- Algebraic structures and combinatorial models
- Limits and Structures in Graph Theory
- Graph theory and applications
- Advanced Topics in Algebra
- Matrix Theory and Algorithms
- Cryptography and Residue Arithmetic
- Magnetic and Electromagnetic Effects
- Hepatitis B Virus Studies
- semigroups and automata theory
- Liver physiology and pathology
- advanced mathematical theories
- DNA and Biological Computing
Nanjing University of Posts and Telecommunications
2018-2024
Nanjing University
2018-2021
Nanjing University of Finance and Economics
2021
China Agricultural University
2019
Let $n$ be a positive integer and $a$ an prime to . Multiplication by induces permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$ Lerch’s theorem gives the sign of this permutation. We explore some applications result problems involving quadratic residues modulo $p$ confirm conjectures posed Sun [‘Quadratic related permutations identities’, Preprint, 2018, arXiv:1809.07766 ]. also study arbitrary $k$ th power primitive roots
The 1-3-5 conjecture of Z.-W. Sun states that any $n\in \mathbb N =\{0,1,2,\ldots \}$ can be written as $x^2+y^2+z^2+w^2$ with $w,x,y,z\in $ such $x+3y+5z$ is a square. In this paper, via the theory ternary quadratic forms and related mo
The evaluations of determinants with Legendre symbol entries have close relation combinatorics and character sums over finite fields. Recently, Sun [9] posed some conjectures on this topic. In paper, we prove also study variants. For example, show the following result:
In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. this paper, by using the arithmetic properties of $p$-th cyclotomic field and finite $\mathbb{F}_p$, we confirm conjecture.
Abstract Motivated by the work initiated Chapman [‘Determinants of Legendre symbol matrices’, Acta Arith. 115 (2004), 231–244], we investigate some arithmetical properties generalised matrices over finite fields. For example, letting $a_1,\ldots ,a_{(q-1)/2}$ be all nonzero squares in field $\mathbb {F}_q$ containing q elements with $2\nmid q$ , give explicit value determinant $D_{(q-1)/2}=\det [(a_i+a_j)^{(q-3)/2}]_{1\le i,j\le (q-1)/2}$ . In particular, if $q=p$ is a prime greater than $3$...
Motivated by the recent work of Zhi-Wei Sun on determinants involving Legendre symbol, in this paper, we study some matrices concerning subgroups finite fields. For example, let $q\equiv 3\pmod 4$ be an odd prime power and $\phi$ unique quadratic multiplicative character field $\mathbb{F}_q$. If set $\{s_1,\cdots,s_{(q-1)/2}\}=\{x^2:\ x\in\mathbb{F}_q\setminus\{0\}\}$, then prove that $$\det\left[t+\phi(s_i+s_j)+\phi(s_i-s_j)\right]_{1\le i,j\le...
Let $q=p^n$ be an odd prime power and let $\mathbb{F}_q$ the finite field of $q$ elements. $\widehat{\mathbb{F}_q^{\times}}$ group all multiplicative characters $\chi$ a generator $\widehat{\mathbb{F}_q^{\times}}$. In this paper, we investigate arithmetic properties certain cyclotomic matrices involving nonzero squares over $\mathbb{F}_q$. For example, $s_1,s_2,\cdots,s_{(q-1)/2}$ any integer $1\le r\le q-2$, define matrix $$B_q(r):=\left[\chi^r(s_i+s_j)+\chi^r(s_i-s_j)\right]_{1\le i,j\le...
Abstract Motivated by the recent work of Zhi-Wei Sun [‘Problems and results on determinants involving Legendre symbols’, Preprint, arXiv:2405.03626], we study some matrices concerning subgroups finite fields. For example, let $q\equiv 3\pmod 4$ be an odd prime power $\phi $ unique quadratic multiplicative character field $\mathbb {F}_q$ . If set $\{s_1,\ldots ,s_{(q-1)/2}\}=\{x^2:\ x\in \mathbb {F}_q\setminus \{0\}\}$ , then prove that $$...
The 1-3-5 conjecture of Z.-W. Sun states that any $n\in\mathbb N=\{0,1,2,\ldots\}$ can be written as $x^2+y^2+z^2+w^2$ with $w,x,y,z\in\mathbb N$ such $x+3y+5z$ is a square. In this paper, via the theory ternary quadratic forms and related modular forms, we study integer version weighted sums four squares certain linear restrictions. Here are two typical results in paper: (i) There finite set $A$ positive integers sufficiently large not $\{16^ka:\ a\in A,\ k\in\mathbb N\}$ $x,y,z,w\in\mathbb...
Let $p$ be an odd prime. For each integer $a$ with $p\nmid a$, the famous Zolotarev's Lemma says that Legendre symbol $(\frac{a}{p})$ is sign of permutation $\Z/p\Z$ induced by multiplication $a$. The extension result to case integers was shown Frobenius. After that, Lerch extended these all positive integers. In this paper we explore some applications Lerch's result. instance, study permutations involving arbitrary $k$-th power residue modulo and primitive roots a $p$. Finally, discuss...
<b><sc>Abstract.</sc></b> Discrete Element Methods (DEM) has been widely used in the field of agricultural equipment design recent years. Thereinto, accurate establishment simulation particles is essential to discrete element simulation. Therefore, by methods combination experiments and real experiments, this paper established broad bean calibrated parameters. By measuring parameters 100-grain weight, three-dimensional size, density, static friction coefficient between seeds Chenghu-14,...
In this paper, we study several topics on additive decompositions of primitive elements in finite fields. Also refine some bounds obtained by Dartyge and Sárközy as well Shparlinski.
Let $d>r\ge 0$ be integers. For positive integers $a,b,c$, if any term of the arithmetic progression $\{r+dn:\ n=0,1,2,\ldots\}$ can written as $ax^2+by^2+cz^2$ with $x,y,z\in\mathbb{Z}$, then form is called $(d,r)$-universal. In this paper, via theory ternary quadratic forms we study $(d,r)$-universality some diagonal conjectured by L. Pehlivan and K. S. Williams, Z.-W. Sun. example, prove that $2x^2+3y^2+10z^2$ $(8,5)$-universal, $x^2+3y^2+8z^2$ $x^2+2y^2+12z^2$ are $(10,1)$-universal...
Let $a,b,c,d,e,f\in\mathbb N$ with $a\ge c\ge e>0$, $b\le a$ and $b\equiv a\pmod2$, $d\le c$ $d\equiv c\pmod2$, $f\le e$ $f\equiv e\pmod2$. If any nonnegative integer can be written as $x(ax+b)/2+y(cy+d)/2+z(ez+f)/2$ $x,y,z\in\mathbb Z$, then the ordered tuple $(a,b,c,d,e,f)$ is said to universal over $\mathbb Z$. Recently, Z.-W. Sun found all candidates for such tuples In this paper, we use theory of ternary quadratic forms show that 44 concrete in Sun's list are indeed For example, prove...