Try this:

#!/usr/bin/perl -w

use strict;

while( <DATA> ) {
    $_ =~ s{^\./}{};     # This regular expression does the work.
    print $_;
}

__DATA__
./file1.txt
file1./file2.log
../file3.txt
file4.cpp
[download]

The work is being done by the line with the comment. The regular expression checks the beginning of each item for the './' and replaces it with nothing if it exists. (The ^ anchors it to the beginning of the line, which is why it doesn't make the replacement where the './' doesn't fall at the beginning of the line.)

Incorporate that regular expression into your loop and you should be good to go.

HTH,

/Larry

Update: Oops! Forgot to backslash the dot in the regex. :)