Estimates for binary quadratic forms and Apollonian circle packings


Salle Kampé de Fériet
Radu Toma
Universität Bonn
Jeudi, 21 Octobre, 2021 - 11:00 - 12:00

Given a positive definite integral binary quadratic form, it is a classical problem in number theory to count the integers that are represented by this form. A modern treatment was given in 2006 by Valentin Blomer and Andrew Granville. This talk will present a way of extending a theorem of Blomer and Granville to obtain estimates for counting proper representations uniform in the (possibly non-fundamental) discriminant. Subsequently, I will give a sketch of how these estimates were used by Jean Bourgain and Elena Fuchs (2011) in proving the positive density conjecture for Apollonian circle packings.