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Estimates for binary quadratic forms and Apollonian circle packings

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Speaker: 
Radu Toma
Affiliation: 
Universität Bonn
Date: 
Wed, 2020-02-05 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

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.
 

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