Structure of the cuspidal rational torsion subgroup of J_1(p^n)

TL;DR

This paper determines the structure of the p-primary part of the cuspidal rational torsion subgroup of the Jacobian of modular curves X_1(p^n) for regular primes p, advancing understanding of torsion in modular Jacobians.

Contribution

It provides a detailed description of the p-primary cuspidal rational torsion subgroup of J_1(p^n), a specific aspect previously not fully characterized.

Findings

Explicit structure of the p-primary subgroup for regular primes p

Extension of known results to higher powers p^n

Enhanced understanding of torsion in modular Jacobians

Abstract

In this article, we determine the structure of the $p$-primary subgroup of the cuspidal rational torsion subgroup of the Jacobian $J_1(p^n)$ of the modular curve $X_1(p^n)$ for a regular prime $p$.