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Overpartitions and class numbers of binary quadratic forms

We show that the Zagier–Eisenstein series shares its nonholomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact formulas, asymptotics, and congruences for the rank differenc...

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Bibliographic Details
Main Authors: Bringmann, Kathrin, Lovejoy, Jeremy
Format: Artigo
Language:Inglês
Published: National Academy of Sciences 2009
Subjects:
Online Access:https://ncbi.nlm.nih.gov/pmc/articles/PMC2666996/
https://ncbi.nlm.nih.gov/pubmed/19336581
https://ncbi.nlm.nih.govhttp://dx.doi.org/10.1073/pnas.0900783106
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