Moonshine at Landau-Ginzburg points

TL;DR

This paper conjectures new relationships between the coefficients of Klein's modular j-function expansions around special points, inspired by mirror symmetry and categorical invariants in mathematical physics.

Contribution

It introduces a novel conjecture linking elliptic expansion coefficients of Klein's j-function at j=0 and j=1728, inspired by recent advances in mirror symmetry and enumerative invariants.

Findings

Proposes a conjecture relating modular function coefficients at special points.

Connects mirror symmetry with properties of Klein's j-function.

Suggests new directions for research in modular forms and mathematical physics.

Abstract

We formulate a conjecture predicting unexpected relationships among the coefficients of the elliptic expansions of Klein's modular j-function around j = 0 and j = 1728. Our conjecture is inspired by recent developments in mirror symmetry, in particular by work of Tu computing categorical enumerative invariants of matrix factorization categories and by work of Li-Shen-Zhou computing FJRW invariants of elliptic curves.