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- W1997626044 abstract "An abelian surface <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is called a QM-abelian surface if its endomorphism ring includes an order of an indefinite quaternion algebra, and a curve <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding=application/x-tex>C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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." @default.
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- W1997626044 date "1999-02-19" @default.
- W1997626044 modified "2023-09-24" @default.
- W1997626044 title "On the Sato-Tate conjecture for QM-curves of genus two" @default.
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- W1997626044 doi "https://doi.org/10.1090/s0025-5718-99-01061-3" @default.
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