### 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 language | English |
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Pages (from-to) | 1649-1662 |

Number of pages | 14 |

Journal | Mathematics of Computation |

Volume | 68 |

Issue number | 228 |

Publication status | Published - 1999 Oct 1 |

### Keywords

- L-functions
- Quaternionic multiplication

### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

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## Cite this

Hashimoto, K. I., & Tsunogai, H. (1999). On the Sato-Tate conjecture for QM-curves of genus two.

*Mathematics of Computation*,*68*(228), 1649-1662.