Dysońs rank, overpartitions, andweakmaass forms

International Mathematics Research Notices

Volumn 2007, Issue , 2007, Pages

  Bringmann, Kathrin ^a   Lovejoy, Jeremy ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951692845     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1093/imrn/rnm063     Document Type: Article

References (34)

1. Andrews, G. E. "On the Theorems of Watson and Dragonette for Ramanujan's Mock Theta Functions." American Journal of Mathematics 88, no.2 (1966): 454-490.
2. Atkin, A. O. L., and H. P. F. Swinnerton-Dyer. "Some Properties of Partitions." Proceedings of the London Mathematical Society 4 (1954): 84-106.
3. Bessenrodt, C., and I. Pak. "Partition Congruences by Involutions." European Journal of Combinatorics 25 (2004): 1139-1149.
4. Brenti, F. "Determinants of Super-Schur Functions, Lattice Paths, and Dotted Plane Partitions." Advances in Mathematics 98 (1993): 27-64.
5. Bringmann, K. "Asymptotics for Rank Partition Functions." Transactions of the American Mathematical Society (forthcoming).
6. Bringmann, K. "Congruences for Dyson's rank." (forthcoming).
7. Bringmann K., and J. Lovejoy. "Rank and Congruences for Overpartition Pairs." International Journal of Number Theory (forthcoming).
8. Bringmann, K., and K. Ono. "The f (q) Mock Theta Function Conjecture and Partition Ranks." Inventiones Mathematicae 165 (2006): 243-266.
9. Bringmann, K., and K. Ono. "Dysons Ranks and Maass Forms." Annals of Mathematics (forthcoming).
10. Bringmann, K., K. Ono, and R. Rhoades. "Eulerian Series as Modular Forms." Journal of American Mathematics Society (forthcoming).
11. Corteel, S., and P. Hitczenko. "Multiplicity and Number of Parts in Overpartitions." Annals of Combinatorics 8 (2004): 287-301.
12. Corteel, S., and J. Lovejoy. "Frobenius Partitions and Ramanujan's 1?1 Summation." Journal of Combinatorial Theory Series A 97 (2002): 177-183.
13. Corteel, S., and J. Lovejoy. "Overpartitions." Transactions of the American Mathematical Society 356 (2004): 1623-1635.
14. Corteel, S., and O.Mallet. "Lattice Paths, Successive Ranks, and Rogers-Ramanujan Identities." Journal of Combinatorial Theory Series A (forthcoming).
15. Desrosiers, P., L. Lapointe, and P.Mathieu. "Jack Polynomials in Superspace."Communications in Mathematical Physics 242 (2003): 331-360.
16. Dyson, F. "Some Guesses in the Theory of Partitions." Eureka (Cambridge) 8 (1944): 10-15.
17. Fortin, J.-F., P. Jacob, and P.Mathieu. "Generating Function for K-Restricted Jagged Partitions." Electronic Journal of Combinatorics 12, no.1 (2005): 17, Research paper R12.
18. Fortin, J.-F., P. Jacob, and P. Mathieu. "Jagged Partitions." Ramanujan Journal 10 (2005): 215-235.
19. Kang, S.-J., and J.-H. Kwon. "Crystal Bases of the Fock Space Representations and String Functions." Journal of Algebra 280 (2004): 313-349.
20. Lovejoy, J. "Overpartitions and Real Quadratic Fields." Journal of Number Theory 106 (2004): 178-186.
21. Lovejoy, J. "Overpartition Theorems of the Rogers-Ramanujan Type." Journal of the London Mathematical Society 69 (2004): 562-574.
22. Lovejoy, J. "Rank and Conjugation for the Frobenius Representation of An Overpartition." Annals of Combinatorics 9 (2005): 321-331.
23. Lovejoy, J., and O. Mallet. "Overpartition Pairs and Two Classes of Basic Hypergeometric Series." AdvanceMathematics (forthcoming).
24. Lovejoy, J., and O. Mallet. "n-Color Overpartitions, Twisted Divisor Functions, and Rogers- Ramanujan Identities." Preprint.
25. Lovejoy, J., and R. Osburn. "Rank Differences for Overpartitions." Quarterly Journal of Mathematics (forthcoming).
26. Newman, M. "Construction and Applications of a Class of Modular Functions. II." Proceedings of the London Mathematical Society 9 (1959): 373-397.
27. Ono, K. "Distribution of the Partition FunctionModulom." Annals of Mathematics 151 (2000): 293-307.
28. Ono, K. "The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series." CBMS Regional Conference Series in Mathematics, 102. Providence, RI: American Mathematical Society, 2004.
29. Pak, I. "Partition Bijections: A Survey." Ramanujan Journal 12 (2006): 5-75.
30. Shimura, G. "On Modular Forms of Half Integral Weight." Annals of Mathematics 97 (1973): 440-481.
31. Treneer, S. "Congruences for the Coefficients ofWeakly HolomorphicModular Forms." Proceedings of the London Mathematical Society 93 (2006): 304-324.
32. Yang, Y. "Transformation Formulas for Generalized Dedekind eta Function." Bulletin of the London Mathematical Society 36 (2004): 671-682.
33. Yee, A.-J. "Combinatorial Proofs of Ramanujan's 1?1 Summation and the q-Gauss Summation." Journal of Combinatorial Theory Series A 105 (2004): 63-77.
34. Zwegers, S. P. "Mock ?-functions and Real Analytic Modular Forms." Pp. 269-277 in ContemporaryMathematics, 291. Proceedings from the Conference on q-serieswith Applications to Combinatorics, Number Theory, and Physics, University of Illinois at Urbana-Champaign, October 26-28, 2000. Providence, RI: AmericanMathematical Society, 2001.