As far as I know - after consulting several different dictionaries - the word Studenter (sic) does not exist in the German language. There is, however, another word for 'a student': Studierende/r (mf). It is one of those pesky nouns that behave like adjectives, and since I have not quite figured out how that works, I do not dare to say anything more specific about how it is used.
It's the actual pronunciation that matters. The first sound in "university" /juːnɪˈvɜːsətiː/ is not a vowel. That's why you need to use "a".