$book =~ s/ü/ü/g;

my $utf8 = qq!<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />!;

$book = "I have changed the most common Unicode characters into HTML entities.\n\nUse this search term to find any leftovers: [€-ÿ]\n\nAlso, don't forget to add a UTF-8 meta tag to your header:\n\n$utf8\n\n".$book;
open (OUT, ">$filename");
print OUT $book;
close OUT;