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In this paper, we study the uniqueness of zero-order entire functions and their difference. We have proved: Let $f(z)$ be a nonconstant entire function of zero order, let $q eq0, eta$ be two finite complex numbers, and let $a$ and $b$ be two distinct complex numbers. If $f(z)$ and $Delta_{q,eta}f(z)$ share $a$, $b$ IM, then $fequiv Delta_{q,eta}f$.
In this paper, we study the uniqueness of meromporphic functions and their difference operators. In particular, We have proved: Let $f$ be a nonconstant entire function on $mathbb{C}^{n}$, let $etain mathbb{C}^{n}$ be a nonzero complex number, and le
It is shown that if equation begin{equation*} f(z+1)^n=R(z,f), end{equation*} where $R(z,f)$ is rational in both arguments and $deg_f(R(z,f)) ot=n$, has a transcendental meromorphic solution, then the equation above reduces into one out of several ty
We consider a family of solutions of $q-$difference Riccati equation, and prove the meromorphic solutions of $q-$difference Riccati equation and corresponding second order $q-$difference equation are concerning with $q-$gamma function. The growth and
This paper establishes a version of Nevanlinna theory based on Jackson difference operator $D_{q}f(z)=frac{f(qz)-f(z)}{qz-z}$ for meromorphic functions of zero order in the complex plane $mathbb{C}$. We give the logarithmic difference lemma, the seco
We construct the Baxters operator and the corresponding Baxters equation for a quantum version of the Ablowitz Ladik model. The result is achieved by looking at the quantum analogue of the classical Backlund transformations. For comparison we find th