This topic probably seems a bit unusual… But in a few weeks I will be touring one of my top choices for college. Through a series of fortunate events, I will be meeting will several professors to discuss the major I intend to pursue and to learn more about the school’s strengths in this field. One of the professors I am meeting with is a Nobel Prize winning scientist who is one of the pioneers of the modern version of my intended field. As it happens, I was reading a great book of his when I found out I would be meeting with him. Would it be in poor taste to ask him at the end of our meeting to autograph this book? I don’t think he would find it offensive, but maybe strange since I doubt his actual students would do such a thing? Any advice is appreciated.
I don’t see anything wrong with it as long as you are polite and respectful. He might even be flattered! 
You’re extremely lucky, so yes, take advantage of the situation.