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Bailey pairs and quantum $q$-series identites. I. The classical identities

Published 25 Sep 2025 in math.NT, math.CA, and math.CO | (2509.21230v1)

Abstract: We use Bailey pairs to prove $q$-series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the study of mock theta functions. In addition to the standard Bailey lemma, we require some changes-of-base established by Bressoud-Ismail-Stanton. We then embed the identities in infinite families using the Bailey chain.

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Authors (2)

  1. Jehanne Dousse 
  2. Jeremy Lovejoy 

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