Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897089 | Journal of Number Theory | 2018 | 35 Pages |
Abstract
Lovejoy and Osburn proved formulas for the generating functions for the rank differences of overpartitions modulo 3 and 5. In this paper, we derive formulas for the generating functions for the rank differences of overpartitions modulo 6 and 10. With these generating functions, we obtain some equalities and inequalities on ranks of overpartitions modulo 6 and 10. We also relate these generating functions to the third order mock theta functions Ï(q) and Ï(q) and the tenth order mock theta functions Ï(q) and Ï(q).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kathy Q. Ji, Helen W.J. Zhang, Alice X.H. Zhao,