19 problems

Zhang et al.'s conjecture. If $f$ and $\Delta^n f$ share $0$ CM, then $f$ has the form

Liu–Laine's conjecture. If $f$ and $\Delta_c^n f$ share $a\in\mathbb{C}\backslash\{0\}$ CM, then

Let $N$ be a positive integer, let $x_i$, $b_i$, $d_i$, and $\overline{d}_i$ be parameters, and let $\mathcal{H}^{{\widehat{\mathfrak{gl}}_N}}(x_i;b_i,d_i,\overline{d}_i,q,\kappa)$…

Let $(C_n)_{n\in\mathbb{N}}$ be the Catalan numbers, and let $d\in\mathbb{N}\!\setminus\!\{0\}$. A sequence is D-algebraic of order $2$ and degree $2d$ if it satisfies a polynomial…

Let $\{F_n\}$, $\{G_n\}$ and $\{H_n\}$ be the sequences of real functions and let $g_n$, $h_n$, $g$, $h$ and $\Theta$ be as in the preceding pointwise convergence conjecture. Assum…

Let $\{F_n\}$, $\{G_n\}$ and $\{H_n\}$ be sequences of real functions on $\{1,\ldots,n\}$ satisfying … Define $g_n(x):=nG_n(\lfloor nx\rfloor)$ and…

Consider the delayed quadratic-rational difference equation referred to as Eq., with parameter $p$, and let $\bar{y}$ denote its equilibrium point. Global stability conjecture. Man…

Grove–Ladas conjecture. No positive non-equilibrium solution has a limit; the question is also to extend and generalize this assertion.

Let $k$ be a positive integer, and consider an additive $2k$th-order difference equation … Here $\mathbf{x}_{n}^{(m,l)}=(x_{n+m},\dots,x_{n+k})$ as defined in the source, and $f$,…

Let $\{x_n\}$ be a positive solution of equation (4ab), and assume that condition (fxp0) holds. Consider its even subsequence $\{x_{2n}\}$ and odd subsequence $\{x_{2n-1}\}$. Parit…

Let $z_{n+1}=\frac{\alpha+\beta z_{n-k}}{\gamma-z_n}$ be the complex rational delay difference equation, where $k$ is the delay and $p$ denotes the period of a periodic solution. E…

Let $z_{n+1}=\frac{\alpha+\beta z_{n-k}}{\gamma-z_n}$ be the complex rational delay difference equation, with parameters $\alpha$, $\beta$, $\gamma$ and delay $k$. A period $p$ is…

Let $f$ be a real-valued Fibonacci function with period $k\in\mathbb{N}$, meaning that … for every $x\in\mathbb{R}$. Let $\phi$ denote the golden ratio. Sroysang's conjecture. … Th…

Consider the difference equation … Here $\alpha$ and $\beta$ are complex parameters, and a solution is called chaotic in the sense used by the paper's numerical dynamical analysis.…

Let $(z_n)$ be a solution of the difference equation … with arbitrary initial values and parameters $\alpha$ and $\beta$ satisfying $\beta=\alpha+1$. Period-two conjecture. All sol…

Let $f:D\to\mathbb{C}$ be a rational function, where $D$ is its natural domain, and assume that $f$ depends effectively on its last variable. Consider the associated difference equ…

The binary-operation identity. The relations

Consider the three difference equations referred to in the source as Eqs. $(1)$, $(8)$ and $(9)$, including the equation … A finite-length cycle means a cycle of finite period, whe…

Let $s_1,s_2$ be generic parameters, and let $\lambda_1,\lambda_2$ satisfy $s_1=tT^{1/2}q^{\lambda_1}$ and $s_2=T^{1/2}q^{\lambda_2}$. Define the series…