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Counting Rational Points on Lines and Conics
23 Apr
23. April 2019
Mathematisch-Physikalisches Kolloquium

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?"


Prof. Roger Heath-Brown/ University of Oxford


Fakultät für Mathematik und Physik


23. April 2019
17:15 Uhr - 18:30 Uhr


Prof. Dr. Ulrich Derenthal
Institut für Algebra, Zahlentheorie und Diskrete Mathematik


Geb.: 1101
Raum: B302
Welfengarten 1
30167 Hannover
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