Shared values of meromorphic functions on a compact Riemann surface

TL;DR

This paper establishes a new bound on shared values of meromorphic functions on compact Riemann surfaces, corrects a previous error, and surveys related research questions.

Contribution

It provides a novel bound for shared values, rectifies an earlier mistake, and offers a comprehensive survey of related problems.

Findings

New bound on shared values of meromorphic functions

Correction of a previous mistake in the literature

Survey of related questions in the field

Abstract

We prove a new bound on the number of shared values of distinct meromorphic functions on a compact Riemann surface, explain a mistake in a previous paper on this topic, and give a survey of related questions.