Daniel Loughran

University of Bath

Rational points on diagonal conics

Heilbronn Number Theory Seminar

7th December 2022, 4:00 pm – 5:00 pm
Fry Building, Fry 1.41

In a 1990 letter, Manin posed Serre the problem of counting the number of diagonal plane conics with a rational point. Serre obtained a sharp upper bound for this problem, and Hooley and Guo independently achieved a sharp lower bound. Recently in joint work with Rome and Sofos, we achieved an asymptotic formula for this counting problem. In this talk I shall explain this formula, and a more general conjectural asymptotic we expect to hold.

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