ZERO-LOCI OF BRAUER GROUP ELEMENTS ON SEMI-SIMPLE ALGEBRAIC GROUPS

Daniel Loughran, Ramin Takloo-Bighash, Sho Tanimoto

Type: Article

Publication Date: 2018-11-29

Citations: 10

DOI: https://doi.org/10.1017/s1474748018000440

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 $\mathbb{Q}$ 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.

Locations

Journal of the Institute of Mathematics of Jussieu - View
arXiv (Cornell University) - View - PDF

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+	Rational Points on Compactifications of Semi-Simple Groups of Rank 1	2004	J. A. Shalika Ramin Takloo-Bighash Yuri Tschinkel
+	Complete symmetric varieties	1983	Corrado De Concini Claudio Procesi
+	Algebraic groups and Discontinuous Subgroups	1966	Armand Borel G. D. Mostow
+	Harmonic Analysis on Semi-Simple Lie Groups II	1972	Garth Warner
+	Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants	2002	Hee Oh
+	Cohomology of Number Fields	2008	Jürgen Neukirch Alexander Schmidt Kay Wingberg
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+ PDF Chat	On the Functional Equations Satisfied by Eisenstein Series	1976	R. P. Langlands