Abstract
LetA be a principally polarized Abelian surface defined over ℚ with End(A) = ℤ andà be the reduction at a good primep. In this paper, we study the density of prime numbersp for which\(\tilde A\left( {\mathbb{F}_p } \right)\) is a cyclic group and establish a conjecture which relates this density.
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The author was supported by the Japan Society for the Promotion of Science Research Fellowships for Young Scientists.
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Yamauchi, T. An observation on the cyclicity of the group of the\(\mathbb{F}_p \)-rational points of Abelian surfaces-rational points of Abelian surfaces. Japan J. Indust. Appl. Math. 24, 307 (2007). https://doi.org/10.1007/BF03167542
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DOI: https://doi.org/10.1007/BF03167542