nLab O'Nan moonshine

Idea

O’Nan moonshine concerns the existence of a graded infinite-dimensional module for the sporadic finite simple group of O’Nan, a so-called pariah group, for which the McKay-Thompson series are weight 3/2 mock modular forms. This form of moonshine relates congruences of McKay-Thompson series and the Selmer and Tate-Shafarevich groups of certain optimal elliptic curves.

Related concepts

• Moonshine
• Mathieu moonshine
• umbral moonshine

References

• John Duncan, Michael Mertens, Ken Ono, O’Nan moonshine and arithmetic, arXiv:1702.03516

For an informal introduction,

• John Duncan, Michael Mertens, Ken Ono, Pariah moonshine, Nature Communications 8: 670 (2017), article, arXiv:1709.08867

For a popular summary,

• Erica Klarreich, Moonshine Link Discovered for Pariah Symmetries, Quanta