Solutions to difference equations have few defects

TL;DR

This paper proves a strong version of Nevanlinna's Second Main Theorem specifically for solutions to certain difference equations where the coefficients grow slowly and the degree condition is met.

Contribution

It extends Nevanlinna theory to difference equations with specific growth and degree conditions, providing new insights into their solutions' value distribution.

Findings

Established a strong form of Nevanlinna's Second Main Theorem for difference equations.

Demonstrated the theorem applies when coefficients grow slowly and R has degree at least 2.

Enhanced understanding of the value distribution of solutions to difference equations.

Abstract

We demonstrate a strong form of Nevanlinna's Second Main Theorem for solutions to difference equations f(z+1)=R(z, f(z)), with the coefficients of R growing slowly relative to f, and R of degree at least 2 in the second coordinate.