Abstract
Here we consider the q-series coming from the Hall-Littlewood polynomials,
These series were defined by Griffin, Ono, and Warnaar in their work on the framework of the Rogers-Ramanujan identities. We devise a recursive method for computing the coefficients of these series when they arise within the Rogers-Ramanujan framework. Furthermore, we study the congruence properties of certain quotients and products of these series, generalizing the famous Ramanujan congruence
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Bruiner J.H., Kohnen W., Ono K.: The arithmetic of the values of modular functions and the divisors of modular forms. Compos. Math. 140(3), 552–566 (2004)
Griffin, M., Ono, K., Warnaar, S.O.: A framework of Rogers-Ramanujan identities and their arithmetic properties. arXiv:1401.7718 [math.NT] (2013)
Hardy G., Wright E.: An Introduction to the Theory of Numbers. 6th edition. Oxford University Press, Oxford (2008)
Ono, K.: The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-series. AMS and CBMS, Providence, RI (2004)
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We would like to thank the NSF for supporting the Emory REU in Number Theory.
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Frechette, C., Locus, M. Combinatorial Properties of Rogers-Ramanujan Type Identities Arising from Hall-Littlewood Polynomials. Ann. Comb. 20, 345–360 (2016). https://doi.org/10.1007/s00026-016-0302-4
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DOI: https://doi.org/10.1007/s00026-016-0302-4