AI Article Synopsis
- Researchers define a method to elevate cuspidal Poincaré series in the context of harmonic weak Maass forms with weight 2 - k for specific values of k.
- This work addresses Dyson's inquiry by providing a framework that helps clarify the mathematical significance of Ramanujan's mock theta functions.
- As a practical outcome, the study reveals that the number of partitions of a positive integer n correlates with singular moduli of a Maass form linked to a weight 4 cusp form from a Calabi-Yau threefold.
Article Abstract
For 2 < k [abstract: see text] we define lifts of cuspidal Poincaré series in S(k)(Gamma(0)(N)) to weight 2 - k harmonic weak Maass forms. This construction answers a question of Dyson by providing the general framework "explaining" Ramanujan's mock theta functions. As an application, we show that the number of partitions of a positive integer n is the "trace" of singular moduli of a Maass form arising from the lift of a weight 4 cusp form corresponding to a Calabi-Yau threefold.
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Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1820651 | PMC |
| http://dx.doi.org/10.1073/pnas.0611414104 | DOI Listing |
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