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Very minor nits
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jirilebl committed May 2, 2022
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Expand Up @@ -16338,7 +16338,7 @@ \subsection{Factorization of sine}
inside the square brackets may differ by a constant.
Since the far left-hand side and the far right-hand side do not have any
logarithms in them they are clearly well-defined.
The equality hods with $g'=0$, which is
The equality holds with $g'=0$, which is
a nice exercise in applying the residue theorem, and we
leave it to the reader.

Expand Down Expand Up @@ -16546,14 +16546,14 @@ \subsection{The product theorem in any open set}
\end{cor}

\begin{proof}
By the product theorem there exists a holomorphic function $h$ that has
By the product theorem, there exists a holomorphic function $h$ that has
zeros exactly where $f$ has poles, and of the same order. The function $fh$
therefore has removable singularities at all the poles of $f$. In other
words, there is a holomorphic $g$ such that $g=fh$.
\end{proof}

\begin{remark}
When we introduced the corollary, we mentioned domain, but then we proved it
When we introduced the corollary, we mentioned \myquote{domain,} but then we proved it
for an open set. The issue is a bit of algebra. If $U$ is not connected,
then the set of holomorphic functions is not an integral domain, it has zero
divisors, and a field of fractions is only defined for integral domains.
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