Probabilities as Values of Modular Forms and Continued Fractions | Zendy

Riad Masri | Zendy; Ken Ono | Zendy

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Probabilities as Values of Modular Forms and Continued Fractions

Author(s) -

Riad Masri,

Ken Ono

Publication year - 2009

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2009/941920

Subject(s) - ramanujan's sum , mathematics , connection (principal bundle) , integer (computer science) , modular form , combinatorics , ramanujan tau function , modular design , ramanujan theta function , pure mathematics , geometry , computer science , programming language , operating system

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

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