#### DOCUMENTA MATHEMATICA, Vol. 21 (2016), 1669-1690

Takao Yamazaki and Yifan Yang

Rational Torsion on the Generalized Jacobian of a Modular Curve With Cuspidal Modulus

We consider the generalized Jacobian \$\widetilde{J}0(N)\$ of a modular curve \$X0(N)\$ with respect to a reduced divisor given by the sum of all cusps on it. When \$N\$ is a power of a prime \$≥ 5\$, we exhibit that the group of rational torsion points \$\widetilde{J}0(N)(\{Q})Tor\$ tends to be much smaller than the classical Jacobian.

2010 Mathematics Subject Classification: Primary 14H40; Secondary 11G16, 11F03, 14G35.

Keywords and Phrases: Generalized Jacobian, torsion points, modular units, cuspidal divisor class.

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