Magnetic orthogonal modular forms

TL;DR

This paper demonstrates that specific meromorphic orthogonal modular forms, related to cusp forms, exhibit magnetic properties characterized by special divisibility in their Fourier coefficients, building on Borcherds' foundational work.

Contribution

It establishes the magnetic nature of certain meromorphic orthogonal modular forms using Borcherds' results, linking divisibility properties to their Fourier coefficients.

Findings

Fourier coefficients satisfy divisibility criteria

Magnetic orthogonal modular forms are counterparts to cusp forms

Borcherds' work implies magneticity

Abstract

In this note we show that certain meromorphic orthogonal modular forms are magnetic, i.e.\ their Fourier coefficients satisfy special divisibility criteria. These meromorphic orthogonal modular forms are counterparts to the orthogonal cusp forms considered by Oda. We show that the seminal of work of Borcherds implies the magneticity of these forms.