Mathematics of Computation

Author(s): Ki-ichiro Hashimoto; Hiroshi Tsunogai.
Journal: Math. Comp. 68 (1999), 1649-1662.
MSC (1991): Primary 11G40; Secondary 11G15, 14H10, 14K15
Posted: February 19, 1999
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Abstract: An abelian surface

is called a QM-abelian surface if its endomorphism ring includes an order of an indefinite quaternion algebra, and a curve

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.

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Retrieve articles in Mathematics of Computation with MSC (1991): 11G40, 11G15, 14H10, 14K15

Ki-ichiro Hashimoto
Affiliation: Department of Mathematics, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan
Email: khasimot@mn.waseda.ac.jp

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