Error "Please insert PRERENDERUNICODE"

This is due to a slight incompatibility of utf8x with amsart (that capitalizes the author's name).

You have two paths to follow:

1. say \usepackage[utf8]{inputenc}

2. make the offending character known to ucs and utf8x before \begin{document}

Path 1 is preferable, if you don't use characters that aren't covered by this option (and even if you do, as it's usually easy to add the needed ones).

If you stick with utf8x, then say as it's said in quite a cryptic way in the output: add

\PrerenderUnicode{ü}

in the preamble (after loading \inputenc). Add all the accented characters that might offend ucs (that's automatically loaded).

if you want to use utf8x you need to also use ucs. However utf8x has not been maintained for a long time and it is much preferable to use utf8 instead:

simply replace

\usepackage[utf8x]{inputenc}

with

\usepackage[utf8]{inputenc}

and it will display properly.