There should be one uniform behavior on all platforms if Python is crossplatoform.

As far as I can understand this issue - unix os.execv() requires "./" to be present to execute anything from current directory. On windows it is enough to specify just filename, but os.execv() doesn't work in this way - is that right and the issue is to make behavior of os.execv() like on windows?

The current behavior definitely needs to be documented.