On the SatoTate conjecture for QMcurves of genus two
Authors:
Kiichiro Hashimoto and Hiroshi Tsunogai
Journal:
Math. Comp. 68 (1999), 16491662
MSC (1991):
Primary 11G40; Secondary 11G15, 14H10, 14K15
Published electronically:
February 19, 1999
MathSciNet review:
1627797
Fulltext PDF Free Access
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Abstract: An abelian surface is called a QMabelian surface if its endomorphism ring includes an order of an indefinite quaternion algebra, and a curve of genus two is called a QMcurve if its jacobian variety is a QMabelian surface. We give a computational result about the distribution of the arguments of the eigenvalues of the Frobenius endomorphisms of QMabelian surfaces modulo good primes, which supports an analogue of the SatoTate Conjecture for such abelian surfaces. We also make some remarks on the field of definition of QMcurves and their endomorphisms.
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Additional Information
Kiichiro Hashimoto
Affiliation:
Department of Mathematics, Waseda University, 341, Ōkubo, Shinjukuku, Tōkyō, 1698555, Japan
Email:
khasimot@mn.waseda.ac.jp
Hiroshi Tsunogai
Affiliation:
Department of Mathematics, Sophia University, 71, Kioichō, Chiyodaku, Tōkyō, 1028554, Japan
Email:
tsuno@mm.sophia.ac.jp
DOI:
http://dx.doi.org/10.1090/S0025571899010613
PII:
S 00255718(99)010613
Keywords:
Quaternionic multiplication,
$L$functions
Received by editor(s):
August 22, 1995
Received by editor(s) in revised form:
January 22, 1998
Published electronically:
February 19, 1999
Article copyright:
© Copyright 1999
American Mathematical Society
