Yuanhong Ren

activity

20162026

most citedQuadratic torsion subgroups of modular Jacobian varieties

1 citations · 1 across the 6 of their papers we have counts for

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math.NT2019

Maximal Eisenstein ideals and cuspidal subgroups of modular Jacobian varieties

Yuan Ren

In this paper, we study the torsion subgroup of $J_{0} (N)$ over the field generated by those points in the cuspidal group, where $N$ is an odd positive integer. We prove that, consid…

math.NT2019★ 1 cited

Quadratic torsion subgroups of modular Jacobian varieties

Yuan Ren

Let $D$ be an odd square-free positive integer and $C$ a divisor of $D$ . For any quadratic character $χ$ modulo $C$ , we prove that the $χ$ -part of the group $J_{0} (D C)_{tor}$ of…

math.NT2017

On the torsion subgroups of the modular Jacobians

Yuan Ren

For any positive integer $N$ , we prove that the rational torsion subgroup of $J_{0} (N)$ agrees with its rational cuspidal subgroups up to a factor of $6 N \prod_{p ∣ N} (p^{2} - 1)$ . More…

math.NT2016

Arithmetic of Eisenstein quotients

Yuan Ren

In this paper, we will study the arithmetic of the Eisenstein part of the modular Jacobians. In the first section, we introduce some general preliminaries of the arithmetic theory…