Complete Classification of Meromorphic Solutions of a Fermat-type Difference Equation
Year: 2026
Type: article
Abstract: We investigate meromorphic solutions of the difference equation f ( z ) 2 + f ( z + c ) = h ( z ) , c ∈ C ∖ { 0 } , $$ \begin{align*} f(z)^2+f(z+c)=h(z), \quad c\in\mathbb C\setminus\{0\}, \end{align*} $$ where h is a transcendental meromorphic function satisfying N ( r , h ) + N ( r , 1 / h ) = S ( r , h ) . $ N(r,h)+N(r,{1}/{h})=S(r,h). $ upper N left parenthesis r comma h right parenthesis plus upper N left parenthesis r comma 1 divided by h right parenthesis equals upper S left parenthesis r comma h right parenthesis period We prove that every solution of hyper-order less than 1 $1$ 1 is of the form f ( z ) = e a z + b − 1 , h ( z ) = e 2 a z + 2 b , $$ \begin{align*} f(z)=e^{az+b}-1, \quad h(z)=e^{2az+2b}, \end{align*} $$
Author: OLEKSANDR VOLKOV
Institution: University of California, Berkeley
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
OpenAlex ID: W7224738554