is the activation server out of action?

No, not according to this site -->Apple - Support - System Status

Here's an Apple tech note on this issue -->If you can't activate your iPhone - Apple Support

Here are some additional observations on possible causes:

• Your version of iTunes is out of date. As of today December 31, 2018, you need iTunes 12.9.2 and it requires Windows 7 or later or Mac OS 10.9.5 or later.
• The phone does not have a valid SIM installed.
• Your antivirus or firewall is blocking access to gs.apple.com. Try temporarily disabling it.
• Your router's firewall is blocking access to gs.apple.com or to a port that it requires (443).
• Your phone is jailbroken, or it was at some time in the past.
• Your computer was used to hack or jailbreak some iOS device in the past (not necessarily the device with the current problem), and its network database was corrupted. Hacking includes using some questionable apps such as recboot, reiboot, Tinyumbrella, redsn0w, etc. If this is a possibility inspect your computer's hosts file. If there are any lines in the file that reference gs.apple.com that is the explanation. You will need to rebuild the hosts file.
• Your phone has a hardware problem. Take it to an Apple store for diagnosis.

Good luck, and Happy New Year