The Monster, the Baby Monster and Traces of Singular Moduli

2017/05/15 by Victor Godet, Godet, Victor
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebra over a field #Algebraic structures and combinatorial models #Art #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Holomorphic function #Literature #Mathematics #Modular form #Moduli #Monster #Number Theory (math.NT) #Physics #Pure mathematics #Quantum mechanics #Representation Theory (math.RT) #hep-th #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1705.05361

arxiv created 2017/05/15 · openalex publication_date 2017/05/15 · arxiv updated 2017/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we provide evidence for new (super) moonshines relating the Monster and the Baby monster to some weakly holomorphic weight 1/2 modular forms defined by Zagier in his work on traces of singular moduli. They are similar in spirit to the recently discovered Thompson moonshine.

Citations

• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
• Monstrous moonshine and monstrous Lie superalgebras
• Super-moonshine for Conway's largest sporadic group
• Umbral Moonshine and the Niemeier Lattices

Related

• From the Monster to Thompson to O'Nan
• Moonshine
• Monstrous Moonshine of higher weight
• Two New Avatars of Moonshine for the Thompson Group
• A short introduction to Monstrous Moonshine