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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

In this paper, we revisit an earlier conjecture by one of us that relatedconjugacy classes of $M_{12}$ to Jacobi forms of weight one and index zero. Weconstruct Jacobi forms for all conjugacy classes of $M_{12}$ that areconsistent with constraints from group theory as well as modularity. However,we obtain 1427 solutions that satisfy these constraints (to the order that wechecked) and are unable to provide a unique Jacobi form. Nevertheless, as aconsequence, we are able to provide a group theoretic proof of the evenness ofthe coefficients of all EOT Jacobi forms associated with conjugacy classes of$M_{12}:2 \subset M_{24}$. We show that there exists no solution where theJacobi forms (for order 4/8 elements of $M_{12}$) transform with phases underthe appropriate level. In the absence of a moonshine for $M_{12}$, we show thatthere exist moonshines for two distinct $L_2(11)$ sub-groups of the $M_{12}$.We construct Siegel modular forms for all $L_2(11)$ conjugacy classes and showthat each of them arises as the denominator formula for a distinctBorcherds-Kac-Moody Lie superalgebra.

Two moonshines for $L_2(11)$ but none for $M_{12}$