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Automatic Proof of Theta-Function Identities

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arxiv 1807.08051 v1 pith:WK7Y6JQ3 submitted 2018-07-20 math.NT

Jie Frye , Frank Garvan This is my paper · ORCID
classification math.NT
keywords identitiesfindpackagefunctionsgeneralizationsgeneralizedproveproving
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This is a tutorial for using two new MAPLE packages, thetaids and ramarobinsids. The thetaids package is designed for proving generalized eta-product identities using the valence formula for modular functions. We show how this package can be used to find theta-function identities as well as prove them. As an application, we show how to find and prove Ramanujan's 40 identities for his so called Rogers-Ramanujan functions G(q) and H(q). In his thesis Robins found similar identities for higher level generalized eta-products. Our ramarobinsids package is for finding and proving identities for generalizations of Ramanujan's G(q) and H(q) and Robin's extensions. These generalizations are associated with certain real Dirichlet characters. We find a total of over 150 identities.

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  1. Machine-Guided Recurrence Boundary Theory for Nahm Sums

    math.NT 2026-08 accept novelty 7.0 of 10

    A recurrence plus two tropical boundary limits reduce Shi and Wang's Conjecture 3.8 for Zagier's twelfth Nahm sum to two generalized-eta identities, which are proved by valence certificates.

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