• Corpus ID: 118015433

# Generalized Andrews-Gordon Identities

@article{Larson2015GeneralizedAI,
title={Generalized Andrews-Gordon Identities},
author={Hannah K. Larson},
journal={arXiv: Number Theory},
year={2015}
}
In a recent paper, Griffin, Ono and Warnaar present a framework for Rogers-Ramanujan type identities using Hall-Littlewood polynomials to arrive at expressions of the form $\sum_{\lambda : \lambda_1 \leq m} q^{a|\lambda|}P_{2\lambda}(1,q,q^2,\ldots ; q^{n}) = \text{"Infinite product modular function"}$ for $a = 1,2$ and any positive integers $m$ and $n$. A recent paper of Rains and Warnaar presents further Rogers-Ramanujan type identities involving sums of terms \$q^{|\lambda|/2}P_{\lambda}(1…
1 Citations
• Joshua Males
• Mathematics
International Journal of Number Theory
• 2019
We introduce and investigate an infinite family of functions which are shown to have generalized quantum modular properties. We realize their “companions” in the lower half plane both as double

## References

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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
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We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's partial fraction
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A (k - 1)-fold Eulerian series expansion is given for II(1 - q(n))(-1), where the product runs over all positive integers n that are not congruent to 0,i or - i modulo 2k + 1. The Rogers-Ramanujan
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We prove a q‐series identity that generalizes Macdonald's A2n(2) η‐function identity and the Rogers–Ramanujan identities. We conjecture our result to generalize even further to also include the