Huaiyin Normal University

output

20082022

most citedTunable double optomechanically induced transparency in an optomechanical system

259 citations

Showing 2016 · math.NTShow all

5 papers · 2 filters

math.NT2016

A kind of orthogonal polynomials and related identities

Zhi-Hong Sun

In this paper we introduce the polynomials ${d_{n}^{(r)} (x)}$ and ${D_{n}^{(r)} (x)}$ given by $d_{n}^{(r)} (x) = \sum_{k = 0}^{n} (k x + r + k) (n - k x - r) (n \geq 0)$ , $D_0^{(r)}(x)=1,…

math.NT2016

New super congruences involving Bernoulli and Euler polynomials

Zhi-Hong Sun

Let $p > 3$ be a prime, and let $a$ be a rational p-adic integer with $a \neq \equiv 0 (mod p)$ . In this paper we establish congruences for $$\sum_{k=1}^{(p-1)/2}\frac{\binom ak\binom{-…

math.NT2016

Proof of a recent conjecture of Z.-W. Sun

Song Guo, Victor J. W. Guo

The polynomials $d_{n} (x)$ are defined by \begin{align*} d_n(x) &= \sum_{k=0}^n{n\choose k}{x\choose k}2^k. \end{align*} We prove that, for any prime $p$ , the following congruences h…

math.NT2016★ 1 cited

Ramanujan's theta functions and sums of triangular numbers

Zhi-Hong Sun

Let $Z$ and $N$ be the set of integers and the set of positive integers, respectively. For $a_{1}, a_{2}, \dots, a_{k}, n \in N$ let $N (a_{1}, a_{2}, \dots, a_{k}; n)$ be the number of…

math.NT2016★ 22 cited

Proof of Sun's conjectures on integer-valued polynomials

Victor J. W. Guo

Recently, Z.-W. Sun introduced two kinds of polynomials related to the Delannoy numbers, and proved some supercongruences on sums involving those polynomials. We deduce new summati…