Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: Ki-ichiro Hashimoto and Hiroshi Tsunogai
Journal: Math. Comp. 68 (1999), 1649-1662
MSC (1991): Primary 11G40; Secondary 11G15, 14H10, 14K15
Published electronically: February 19, 1999
MathSciNet review: 1627797
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

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

Retrieve articles in all journals with MSC (1991): 11G40, 11G15, 14H10, 14K15


Additional Information

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

Hiroshi Tsunogai
Affiliation: Department of Mathematics, Sophia University, 7-1, Kioi-chō, Chiyoda-ku, Tōkyō, 102-8554, Japan
Email: tsuno@mm.sophia.ac.jp

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01061-3
PII: S 0025-5718(99)01061-3
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