We offer two types of authentication. Mendeley is easy. When you sign up for Mendeley, you can simply use your existing email address.
Google is a bit of a different story. Your @gmail.com is also a Google account, but certainly not the only possible option. When you sign up for a Google account, note that it will pre-fill the username box with @gmail.com. By default, it will create a Gmail account too. However, note the little link below that box "I rather use my existing email address". Click that and Google will allow you to create a Google account using your existing email address.