English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For a positive integer $N$, let $\mathscr{C}_N(\mathbb{Q})$ be the rationalcuspidal subgroup of $J_0(N)$ and $\mathscr{C}(N)$ be the rational cuspidaldivisor class group of $X_0(N)$, which are both subgroups of the rationaltorsion subgroup of $J_0(N)$. We prove that two groups$\mathscr{C}_N(\mathbb{Q})$ and $\mathscr{C}(N)$ are equal when $N=p^2M$ forany prime $p$ and any squarefree integer $M$. To achieve this we show that allmodular units on $X_0(N)$ can be written as products of certain functions$F_{m, h}$, which are constructed from generalized Dedekind eta functions.Also, we determine the necessary and sufficient conditions for such products tobe modular units on $X_0(N)$ under a mild assumption.

The rational cuspidal subgroup of $J_0(p^2M)$ with $M$ squarefree