The default shipping of gnome-shell in Ubuntu 13.04 is a mix of version 3.6 and version 3.8. We can upgrade to a general (and maybe clean) Ubuntu/GNOME system via ppa. Reference: How To Upgrade to GNOME 3.8 in Ubuntu 13.04.
# add-apt-repository ppa:gnome3-team/gnome3
# apt-get update && apt-get install gnome-shell ubuntu-gnome-desktop
# apt-get dist-upgrade
# apt-get autoremove && apt-get autoclean
After installation and reboot your system, you can login into the Ubuntu/GNOME environment.
However, the default login manager may be use the lightdm rather than GDM. You should reconfigure it manually if you want to use GDM and the configuration prompt is not shown while installation. The command is:
When the prompt shown which is similar as the reference page one, select GDM. Reboot your system then you can use the default login manager.
Then we encounter another problem. In previous use of lightdm, Ubuntu will connect to network as possible. However in GDM that it will not do that procedure. If we want to let Ubuntu/GNOME/GDM connect to network for access like SSH, we can add a autostart symlink for it. Reference page: How can I use NetworkManager in GDM?.
And everything works as usual.
Enjoy it. 😉