"Counting Rational Points on Lines and Conics"
Speaker:Prof. Roger Heath-Brown, University of Oxford
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Let N(B) be the number of rational points (u/w,v/w) on the line ax+by+c=0 with |u|,|v|,|w| all at most B. We ask:- "How does N(B) grow as B tends to infinity?" The answer to this has been well understood for some time, but displays some subtleties. We then turn to the corresponding question for conics Q(x,y)=0, where it is known that N(B) is asymptotic to cB as B tends to infinity (provided there is at least one rational point). We ask "How large must B be in terms of Q for one to see this behaviour?", and "What happens for smaller values of B?"
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Direct link to event:https://events.goettingen-campus.de/event?eventId=16890