Rademacher Sums and Rademacher Series

Authors
Publication date 2014
Host editors
  • W. Kohnen
  • R. Weissauer
Book title Conformal Field Theory, Automorphic Forms and Related Topics : CFT 2011, Heidelberg, September 19-23, 2011
ISBN
  • 9783662438305
Series Contributions in Mathematical Contributions in Mathematical, 8
Pages (from-to) 143-182
Number of pages 40
Publisher Heidelberg: Springer
Organisations
  • Faculty of Science (FNWI) - Institute of Physics (IoP) - Institute for Theoretical Physics Amsterdam (ITFA)
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.
Document type Chapter
Language English
Published at https://doi.org/10.1007/978-3-662-43831-2_6
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