Finding (correct) citation info for math references
For mathematical articles I'm not aware of any citation database of (nearly) as good quality as MatSciNet --- your university is probably also paying a significant subscription fee for it.

As Paul Garrett already mentioned, you can probably access it from home via your university's library. There is actually an even simpler method (at least with a laptop): while at your university you can "pair your device" to automatically have access under your university account for 90 days, when you need to repair it. See the green/blue icon in the top-left corner of MathSciNet, linking to http://www.ams.org/pairing/pair_my_device.html

If you have a desktop at home, you might also do this though a VPN or library site of the university, and then you're set for the next 90 days.