Zhi-Wei Sun

activity

20082013

most citedOn sums of primes and triangular numbers

17 citations · 36 across the 8 of their papers we have counts for

collaborators

9 papers

math.NT2013★ 1 cited

On some determinants with Legendre symbol entries

Zhi-Wei Sun

In this paper we mainly focus on some determinants with Legendre symbol entries. Let $p$ be an odd prime and let $(\frac{\cdot}{p})$ be the Legendre symbol. We show that $(\frac{-S(d…

math.NT2012

On a pair of zeta functions

Zhi-Wei Sun

Let $m$ be a positive integer, and define $$ζ_m(s)=\sum_{n=1}^\infty\frac{(-e^{2πi/m})^{ω(n)}}{n^s}\ \ \ \ \text{and} \ \ \ \ ζ^*_m(s)=\sum_{n=1}^\infty\frac{(-e^{2πi/m})^{Ω(n)}}{n…

math.NT2010★ 5 cited

Congruences involving generalized central trinomial coefficients

Zhi-Wei Sun

For integers $b$ and $c$ the generalized central trinomial coefficient $T_{n} (b, c)$ denotes the coefficient of $x^{n}$ in the expansion of $(x^{2} + b x + c)^{n}$ . Those $T_n=T_n(1,1)\ (n=0,1,2…

math.NT2010★ 2 cited

On divisibility concerning binomial coefficients

Zhi-Wei Sun

Let k and n be positive integers. We mainly show that $(l n + 1) ∣ k (k n k n + l n),$ $2 (n k n) ∣ (n 2 n) C_{2 n}^{(k - 1)}$ , $(n k n) ∣ (2 k - 1) C_{n} (2 n 2 k n),$ …

math.NT2009★ 6 cited

Fibonacci numbers modulo cubes of primes

Zhi-Wei Sun

Let $p$ be an odd prime. It is well known that $F_{p - (\frac{p}{5})} \equiv 0 (mod p)$ , where ${F_{n}}_{n \geq 0}$ is the Fibonacci sequence and $(-)$ is the Jacobi symbol. In this paper w…

math.NT2009★ 4 cited

Some curious congruences modulo primes

Li-Lu Zhao, Zhi-Wei Sun

Let n be a positive odd integer and let p>n+1 be a prime. We mainly derive the following congruence: $0 < i_{1} < ... < i_{n} < p \sum (i_{1} /3) (- 1)^{i_{1}} / (i_{1} ... i_{n}) = 0 (m o d p) .$