Rademacher Sums and Rademacher Series
Number Theory
2012-10-12 v1 High Energy Physics - Theory
Representation Theory
Abstract
We exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms. We introduce the notion of Rademacher series and describe several applications, including the determination of coefficients of Rademacher sums and a very general form of Zagier duality. We then review the application of Rademacher sums and series to moonshine both monstrous and umbral and highlight several open problems. We conclude with a discussion of the interpretation of Rademacher sums in physics.
Keywords
Cite
@article{arxiv.1210.3066,
title = {Rademacher Sums and Rademacher Series},
author = {Miranda C. N. Cheng and John F. R. Duncan},
journal= {arXiv preprint arXiv:1210.3066},
year = {2012}
}
Comments
46 pages