You need to use double quotes so Perl will interpolate the variables inside the string.

print redirect("$referring_url&alert=3");
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Single quotes mean a literal string which is exactly what you got in the second case. In the first case, Perl interprets it as perl code. This is the error I get when running the snippet:

Operator or semicolon missing before &variable at -e line 1.
Ambiguous use of & resolved as operator & at -e line 1.
Can't modify bitwise and (&) in scalar assignment at -e line 1, near "
+value)"
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With Perl, it you get a "500 Server Error", it means that the script died. You should look in the web server error log, or run the script from the command line, to figure out why it died.