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

Ki Ichiro Hashimoto, Hiroshi Tsunogai

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1649-1662
ページ数14
ジャーナルMathematics of Computation
68
228
DOI
出版ステータスPublished - 1999 10
外部発表はい

ASJC Scopus subject areas

  • 代数と数論
  • 計算数学
  • 応用数学

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