Probabilities as Values of Modular Forms and Continued Fractions
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/941920 |
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| _version_ | 1832560296267350016 |
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| author | Riad Masri Ken Ono |
| author_facet | Riad Masri Ken Ono |
| author_sort | Riad Masri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1601f80ef8394cbda778f5e2c3b2b71b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1601f80ef8394cbda778f5e2c3b2b71b2025-02-03T01:27:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/941920941920Probabilities as Values of Modular Forms and Continued FractionsRiad Masri0Ken Ono1Department of Mathematics, University of Wisconsin, Madison, WI 53706, USADepartment of Mathematics, University of Wisconsin, Madison, WI 53706, USAWe 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.http://dx.doi.org/10.1155/2009/941920 |
| spellingShingle | Riad Masri Ken Ono Probabilities as Values of Modular Forms and Continued Fractions International Journal of Mathematics and Mathematical Sciences |
| title | Probabilities as Values of Modular Forms and Continued Fractions |
| title_full | Probabilities as Values of Modular Forms and Continued Fractions |
| title_fullStr | Probabilities as Values of Modular Forms and Continued Fractions |
| title_full_unstemmed | Probabilities as Values of Modular Forms and Continued Fractions |
| title_short | Probabilities as Values of Modular Forms and Continued Fractions |
| title_sort | probabilities as values of modular forms and continued fractions |
| url | http://dx.doi.org/10.1155/2009/941920 |
| work_keys_str_mv | AT riadmasri probabilitiesasvaluesofmodularformsandcontinuedfractions AT kenono probabilitiesasvaluesofmodularformsandcontinuedfractions |