Counting Rational Points on Lines and Conics
Abstract: 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?"
Speaker
Prof. Roger Heath-Brown/ University of Oxford
Organiser
Fakultät für Mathematik und Physik
Date
23. April 201917:15 o'clock - 18:30 o'clock
Public contact
Prof. Dr. Ulrich DerenthalInstitut für Algebra, Zahlentheorie und Diskrete Mathematik
Location
WelfenschlossBuilding: 1101
Room: B302
Welfengarten 1
30167 Hannover