|Keep It Simple, Stupid|
As others before me have mentioned, all three options are valid syntax, but you probably already knew that. So, it comes down to matters of style. Where style is concerned, perlstyle is the go-to document.
perlstyle doesn't specify this case. However, a couple of quotes hint that parenthesis might be slightly preferred:
Function and method names seem to work best as all lowercase. E.g., $obj->as_string() .
This example uses parens.
Note that function names are considered more readable with parentheses after their name, that is function() .
This quote comes from the Pod doc section, where functions are referred to in English (or whatever) text, so it doesn't exactly refer to the code itself.
The bottom line, the golden rule with any stylistic choice, is be consistent. If you (or someone else) starts coding with or without parenthesis, keep doing it.
In reply to Re: Handling braces with methods without arguments