Probabilities as Values of Modular Forms and Continued Fractions. (31st August 2009)

• Record Type: Journal Article
• Authors: Masri, Riad; Ono, Ken
• Other Names: Haukkanen Pentti Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2009(2009)
• Publication Date: 2009-08-31
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2009/941920
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : We consider certain probability problems which are naturally related to integer partitions. We show that the corresponding probabilities are values of classical modular forms. Thanks to this connection, we then show that certain ratios of probabilities are specializations of the Rogers-Ramanujan and Ramanujan- Selberg- Gordon-Göllnitz continued fractions. One particular evaluation depends on a result from Ramanujan's famous first letter to Hardy.