What do you mean by "zero"? Truncate to zero length? Delete?
open my $fh, ">myfile"; # will truncate by opening it for write acces
truncate "myfile", 0; # will truncate (if it's implemented on your
unlink "myfile"; # will remove it
FYI, under unix file ownership has little to do with being able to trucate or delete it. If you are root, you can do either. Otherwise, to truncate you'll need to have write access to the file. To delete it, you'll need write and execute access to the file's parent directory.