A framework of Rogers-Ramanujan identities and their arithmetic properties

Griffin, Michael J., Ono, Ken and Warnaar, S. Ole (2016) A framework of Rogers-Ramanujan identities and their arithmetic properties. Duke Mathematical Journal, 165 8: 1475-1527. doi:10.1215/00127094-3449994

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Author Griffin, Michael J.
Ono, Ken
Warnaar, S. Ole
Title A framework of Rogers-Ramanujan identities and their arithmetic properties
Journal name Duke Mathematical Journal   Check publisher's open access policy
ISSN 0012-7094
Publication date 2016-06-01
Year available 2016
Sub-type Article (original research)
DOI 10.1215/00127094-3449994
Open Access Status Not Open Access
Volume 165
Issue 8
Start page 1475
End page 1527
Total pages 53
Place of publication New York, NY United States
Publisher Econometric Society
Language eng
Subject 2600 Mathematics
Abstract The two Rogers-Ramanujan q-series where σ 0; 1, play many roles in mathematics and physics. By the Rogers- Ramanujan identities, they are essentially modular functions. Their quotient, the Rogers-Ramanujan continued fraction, has the special property that its singular values are algebraic integral units. We find a framework which extends the Rogers- Ramanujan identities to doubly infinite families of q-series identities. If a ∈ (1, 2) and m, n ≥ 1, then we have [infinite product modular function], where the P λ(x, x, ...; q) are Hall-Littlewood polynomials. These q-series are specialized characters of affine Kac-Moody algebras. Generalizing the Rogers- Ramanujan continued fraction, we prove in the case of A that the relevant q-series quotients are integral units.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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