期刊论文详细信息
JOURNAL OF NUMBER THEORY 卷:190
Rational torsion subgroups of modular Jacobian varieties
Article
Ren, Yuan1 
[1] Sichuan Normal Univ, Sch Math Sci, Chengdu, Sichuan, Peoples R China
关键词: Modular curve;    Generalized Ogg's conjecture;    Eisenstein ideal;   
DOI  :  10.1016/j.jnt.2018.02.009
来源: Elsevier
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【 摘 要 】

In this article, we study the Q-rational torsion subgroups of the Jacobian varieties of modular curves. The main result is that, for any positive integer N, J(0)(N)(Q)(tor)[q(infinity)] = 0 if q is a prime not dividing 6 . N . Pi(p)(vertical bar N)(p(2) - 1). To prove the result, we explicitly construct a collection of Eisenstein series with rational Fourier expansions, and then determine their constant terms to control the size of the rational torsion subgroups. (C) 2018 Elsevier Inc. All rights reserved.

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