On the Sato-Tate conjecture for QM-curves of genus two

Kiichiro Hashimoto, Hiroshi Tsunogai

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    An abelian surface A is called a QM-abelian surface if its endomorphism ring includes an order of an indefinite quaternion algebra, and a curve C of genus two is called a QM-curve if its jacobian variety is a QM-abelian surface. We give a computational result about the distribution of the arguments of the eigenvalues of the Frobenius endomorphisms of QM-abelian surfaces modulo good primes, which supports an analogue of the Sato-Tate Conjecture for such abelian surfaces. We also make some remarks on the field of definition of QM-curves and their endomorphisms.

    Original languageEnglish
    Pages (from-to)1649-1662
    Number of pages14
    JournalMathematics of Computation
    Volume68
    Issue number228
    Publication statusPublished - 1999 Oct

    Fingerprint

    Abelian Surfaces
    Genus
    Curve
    Endomorphisms
    Jacobian Varieties
    Quaternion Algebra
    Endomorphism Ring
    Frobenius
    Algebra
    Computational Results
    Modulo
    Analogue
    Eigenvalue

    Keywords

    • L-functions
    • Quaternionic multiplication

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Applied Mathematics
    • Computational Mathematics

    Cite this

    On the Sato-Tate conjecture for QM-curves of genus two. / Hashimoto, Kiichiro; Tsunogai, Hiroshi.

    In: Mathematics of Computation, Vol. 68, No. 228, 10.1999, p. 1649-1662.

    Research output: Contribution to journalArticle

    Hashimoto, Kiichiro ; Tsunogai, Hiroshi. / On the Sato-Tate conjecture for QM-curves of genus two. In: Mathematics of Computation. 1999 ; Vol. 68, No. 228. pp. 1649-1662.
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