I am currently struggling to understand Section 11.9 in Tom Apostol's Introduction to Analytic Number Theory, where he talks about taking the logarithm of a Dirichlet series.  The idea is that we have some Dirichlet series $F(s) = \sum_{n=1}^\infty f_nn^{-s}$ with $f(1)\neq 0$ and   $F(s)$ is absolutely convergent  $F(s) \neq 0$   for any $s$ with $\mathfrak{R}(s)&gt;\sigma_0$.  Apostol says that we can then always find some Dirichlet series $G(s)$ that is also absolutely convergent for $\mathfrak{R}(s)&gt;\sigma_0$ and fulfils $e^{G(s)} = F(s)$ for any such $s$, and that $$G(s) = \ln f(1) + \sum_{n=2}^\infty \frac{(f' * f^{-1})(n)}{\ln n} n^{-s}$$ where $f^{-1}$ is the Dirichlet inverse of $f$ and $f'(n) = f(n) \ln n$, i.e. they correspond to the multiplicative inverse and the negative derivative of $F$.  However, if I am not missing anything here, I think all of this only works if $\sum_{n=1}^\infty f'(n) n^{-s}$ and $\sum_{n=1}^\infty f^{-1}(n) n^{-s}$ converge absolutely, but I don't see why they should, in general.
An excerpt from Introduction to Analytic Number Theory by Tom M. Apostol.      I have three main concerns regarding this proof:    What is the abscissa of convergence for $\frac{1}{F(s)}$ - why can we take the product of the two series. I only know this is true if the two series are absolutely convergent.  Why can we do term by term integration? I believe its suffices to show that the series converges locally uniformly - BUT is this true?  How does the proof show that $G(s)$ converges uniformly?
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However even though I can view the contents of the .rar archive in the Archive Manager, I am unable to extract it due to this error:    The archive should contain two folders within it, each though contain at least 10 audio files as well as a PDF file each (I don't know what the contents exactly should be except for there should be audio files in there, and the content I have described is what I can see from the Archive Manager's view). So the only thing I am left with except the error is one of the folders and one of the audio files, but it says it has 0 bytes in it.  So how exactly do I fix this problem? I am running Ubuntu GNOME 16.04.1 with GNOME 3.20.  Information Update:  In reply to a comment requesting the output from the dpkg -l unrar unrar-free command:  Desired=Unknown/Install/Remove/Purge/Hold | Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend |/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad) ||/ Name           Version      Architecture Description +++-==============-============-============-================================= un  unrar          &lt;none&gt;       &lt;none&gt;       (no description available) dpkg-query: no packages found matching unrar-free I'm flying Etihad Airways to Melbourne and I've a 14 hours layover at Abu Dhabi.  Some say that as long as you are inside the airport terminal you don't require a transit visa while some say you need a transit visa if your layover is more than 10 hours.  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Word for the behavior of people who complain at everything you do Selection Tool doesn't rotate in Illustrator Why my selection tool doesn't rotate object? I selected the object and it doesn't work. How do I fix this? Enable 'on the fly' CRS transformation in QGIS 3? I want to utilize beamer's \uncover command within ChemFig's reaction scheme environment, i.e.:  \schemestart     \chemname[-1ex]{\chemfig[][scale=1]{*5(-=(-=[:-60]O)-O-=)}}{Furfural}     \uncover&lt;2-&gt;{         \arrow(furfural--mf){-&gt;[*{0}HDO][]}         \chemname[-1ex]{\chemfig{*5(-=(-)-O-=)}}{2-Methylfuran}     } \schemestop   However, this results in numerous "undefined control sequence" errors.  Is there a way to use beamer's \uncover command within ChemFig?  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