Receiving this error in latex for "missing $ inserted" and that "You need to enclose all mathematical expressions.."

Question

This is latex Overleaf and I'm receiving this error with no idea on how to fix it

edit: Here is the code

\begin{definition}[Dirichlet Character]
Any map $\chi:(\mathbb{Z}/n\mathbb{Z})* \rightarrow \mathbb{C}$ is said to be a Dirichlet Character of modulus $n$ if for any two integers $a$ and $b$,

\begin{itemize}

\item $\chi(ab) = \chi(a)\chi(b) \hspace{2pt} \text{(multiplicity)}$ 
\item $\chi(a)$ = $\begin{cases}
$0$ & \text{if } $\gcd(a,n) > 1$ \\
\text{non-zero} & \text{if }$\gcd(a,n) = 1$ \\
\end{cases}$    \item $\chi(a+m)$ = $\chi(a)$ \text{(periodic with period $m$)}
\end{itemize}

\end{definition}

Answer 1

This works, because each equations are in one math environment (see @DavidCarlisle comment):

\documentclass{article}
\usepackage{amsmath, amssymb, amsthm}
\theoremstyle{definition}  % for upright text in definition
\newtheorem{definition}{Definition}

\begin{document}
\begin{definition}[Dirichlet Character]
Any map $\chi:(\mathbb{Z}/n\mathbb{Z})* \rightarrow \mathbb{C}$ is said to be a Dirichlet Character of modulus $n$ if for any two integers $a$ and $b$,
    \begin{itemize}
\item $\chi(ab) = \chi(a)\chi(b)$ \quad(multiplicity)
\item $\chi(a) = \begin{cases}
            0   & \text{if } \gcd(a,n) > 1  \\
          \ne 0 & \text{if } \gcd(a,n) = 1  \\
                 \end{cases}$    
\item $\chi(a+m) = \chi(a)$      \quad(periodic with period $m$)
    \end{itemize}
\end{definition}
\end{document}

Edite: Considered @Mico comment.