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.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/246