Zero-loci of Brauer group elements on semi-simple algebraic groups

Daniel Loughran, Ramin Takloo-Bighash, Sho Tanimoto

    Research output: Contribution to journalArticlepeer-review

    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 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.

    Original languageEnglish
    Pages (from-to)1-41
    Number of pages41
    JournalJournal of the Institute of Mathematics of Jussieu
    Early online date29 Nov 2018
    DOIs
    Publication statusPublished - 29 Nov 2018

    Keywords

    • 14F22
    • 2010 Mathematics subject classification:
    • Primary 14G05
    • Secondary 11D45

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