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

Ki Ichiro Hashimoto, Hiroshi Tsunogai

Research output: Contribution to journalArticlepeer-review

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
DOIs
Publication statusPublished - 1999 Oct

Keywords

  • L-functions
  • Quaternionic multiplication

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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