Lin, A and McSpirit, E and Vishnu, A (2020) Algebraic relations between partition functions and the j-function. In: Research in Number Theory, 6 (1).
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Abstract
We obtain identities and relationships between the modular j-function, the generating functions for the classical partition function and the Andrews spt-function, and two functions related to unimodal sequences and a new partition statistic we call the “signed triangular weight” of a partition. These results follow from the closed formula we obtain for the Hecke action on a distinguished harmonic Maass form M(τ) defined by Bringmann in her work on the Andrews spt-function. This formula involves a sequence of polynomials in j(τ) , through which we ultimately arrive at expressions for the coefficients of the j-function purely in terms of these combinatorial quantities. © 2019, Springer Nature Switzerland AG.
| Item Type: | Journal Article |
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| Publication: | Research in Number Theory |
| Publisher: | Springer |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Harmonic Maass forms; Modular forms; Partitions; Spt function |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 24 Jan 2023 11:08 |
| Last Modified: | 24 Jan 2023 11:08 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79421 |
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