Zero-loci of Brauer group elements on semi-simple algebraic groups
Number Theory
2018-10-09 v2 Algebraic Geometry
Abstract
We consider the problem of counting the number of rational points of bounded height in the zero-loci of Brauer group elements on semi-simple algebraic groups over number fields. We obtain asymptotic formulae for the counting problem for wonderful compactifications using the spectral theory of automorphic forms. Applications include asymptotic formulae for the number of matrices over Q whose determinant is a sum of two squares. These results provide a positive answer to some cases of a question of Serre concerning such counting problems.
Keywords
Cite
@article{arxiv.1705.09244,
title = {Zero-loci of Brauer group elements on semi-simple algebraic groups},
author = {Daniel Loughran and Ramin Takloo-Bighash and Sho Tanimoto},
journal= {arXiv preprint arXiv:1705.09244},
year = {2018}
}
Comments
35 pages. Added more details and fixed typos. Final version