International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 941920, 11 pages
doi:10.1155/2009/941920
Research Article

Probabilities as Values of Modular Forms and Continued Fractions

Riad Masri and Ken Ono

Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA

Received 12 May 2009; Accepted 26 August 2009

Academic Editor: Pentti Haukkanen

Copyright © 2009 Riad Masri and Ken Ono. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. E. Holroyd, T. M. Liggett, and D. Romik, “Integrals, partitions, and cellular automata,” Transactions of the American Mathematical Society, vol. 356, no. 8, pp. 3349–3368, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. G. E. Andrews, “Partitions with short sequences and mock theta functions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 13, pp. 4666–4671, 2005. View at Zentralblatt MATH · View at MathSciNet
  3. K. Bringmann and K. Mahlburg, “Asymptotics for partitions without sequences,” preprint.
  4. G. E. Andrews, H. Eriksson, F. Petrov, and D. Romik, “Integrals, partitions and MacMahon's theorem,” Journal of Combinatorial Theory. Series A, vol. 114, no. 3, pp. 545–554, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Lang, Elliptic Functions, vol. 112 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2nd edition, 1987. View at MathSciNet
  6. A. Selberg, “Über einge arithmetische Identitäten,” Avh. Norske Vidensk. Akad, vol. 23, no. 8, 1936.
  7. A. Folsom, Modular units, Ph.D. thesis, University of California, Los Angeles, Calif, USA, 2006.
  8. D. J. Newman, Analytic Number Theory, vol. 177 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1998. View at MathSciNet
  9. K. Ono, The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-Series, vol. 102 of CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, USA, 2004. View at MathSciNet
  10. G. E. Andrews, B. C. Berndt, L. Jacobsen, and R. L. Lamphere, “The continued fractions found in the unorganized portions of Ramanujan's notebooks,” in Memoirs of the American Mathematical Society, vol. 99, American Mathematical Society, Providence, RI, USA, 1992.
  11. H. Göllnitz, “Partitionen mit Differenzenbedingungen,” Journal für die Reine und Angewandte Mathematik, vol. 225, pp. 154–190, 1967. View at Zentralblatt MATH · View at MathSciNet
  12. S. Ramanujan, Collected Papers, Chelsea, NY, USA, 1962.