The context of the question is that you have unexpectedly run across a word you need to look up - so you are asking somebody if they have a dictionary, any dictionary. The emphasis is whether they even have one.
Would it be "У тебя есть словарь?"
Now, let's say you have been sharing a dictionary with another student. You have both been using it. You need it again but you can't find it. You ask the person "Do you have the dictionary?"
The context of the question is that there is a clear understanding that there is a dictionary. You even know which dictionary you're talking about. You're simply wondering if they have that dictionary.
Again, would it be "У тебя есть словарь?"
If so, then how do Russians convey the idea of specificity with regards to such questions as we can in English?