[Abstract] F.G. Garvan; Weighted partition identities and divisor sums, in "Frontiers in Orthogonal Polynomials and q-Series", Proceedings of a Conference in honor of Mourad Ismail for his 70th birthday, Orlando, May 10-12, 2015, World Scientic, to appear.


Abstract:

We prove two one-parameter $q$-series identities which specialize to four weighted partition identities. Three of the weighted partition identities have coefficients which are divisor sums. The other is an identity originally due to Alladi whose right side is Gauss's triangular number series. Some of the proofs depend on $q$-series results related to the arithmetic of $\mathbb{Q}[\sqrt{2}]$ due to Lovejoy and due to Corson, Favero, Liesinger and Zubairy.

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Created by F.G. Garvan (fgarvan@ufl.edu) on Monday, May 16, 2016.
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