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Determinants as sums of two squares

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Speaker: 
Daniel Loughran
Affiliation: 
University of Manchester
Date: 
Wed, 2019-01-16 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

A classical theorem due independently to Landau and Ramanujan 
gives an asymptotic formula for the number of integers which can be 
written as a sum of two squares. We prove an analogous result for the 
determinant of a matrix using the spectral theory of automorphic forms. 
This is a special case of a more general result on a problem of Serre 
concerning specialisations of Brauer group elements on semisimple 
algebraic groups. This is joint work with Sho Tanimoto and Ramin 
Takloo-Bighash.

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