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\title{Gauss Sums and the P\'olya--Vinogradov Inequality}
\author{Rodrigo Raya and Manuel Eberl}
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\begin{abstract}
This article provides a full formalisation of Chapter 8 of Apostol's \emph{Introduction to Analytic Number Theory}~\cite{apostol1976analytic}.
Subjects that are covered are:
\begin{itemize}
\item periodic arithmetic functions and their finite Fourier series
\item (generalised) Ramanujan sums
\item Gauss sums and separable characters
\item induced moduli and primitive characters
\item the P\'olya--Vinogradov inequality
\end{itemize}
\end{abstract}

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