Roger Heath-Brown

University of Oxford

Counting Rational Points on Conics

Heilbronn Number Theory Seminar

27th February 2019, 4:00 pm – 5:00 pm
Howard House, 4th Floor Seminar Room

Rational points on conics can be represented by primitive integer triples (x,y,z) satisfying Q(x,y,z)=0 for a given nonsingular (integral) quadratic form Q. If there are N(B) points with max(|x|,|y|,|z|) at most B, then 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?", "What happens for smaller values of B?", and "What other questions does this help with?"TBA

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