I agree that you need to acquire ownership if the original author is unavailable now. Double-check that by posting to firstname.lastname@example.org mailing list to make certain.
Then fix the bug and documentation error before re-writing and re-factoring code. It's only one extra version upload, and it lets the module's users know that you are making changes and lets them prepare for those changes.
I also have ex-Fortran code in Perl, and the sensible process there is to make the basic, obvious changes (change loops to use the '..' operator; fix variable names to something meaningful instead of single letters; lexicalize function variables that are only found within an individual loop down to that loop).
(Looking at Math-Brent's code, it looks like the original author already did some of that, although it seems in some cases he has multiple variables in play where an array would be more useful).
Then consider OO-ing the code.
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