Bressoud's identities for even moduli. New companions and related positivity results

2021/11/27 by Alexander Bérkovich, Berkovich, Alexander · 1 citation
Mathematics · #05A30 #11B65 #11P84 #33D1 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2111.13994

openalex publication_date 2021/11/27 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

I revisit Bressoud's generalised Borwein conjecture. Making use of certain positivity-preserving transformations for q-binomial coefficients, I establish the truth of infinitely many new cases of the Bressoud conjecture. In addition, I prove new doubly-bounded refinement of the Foda-Quano identities. Finally, I discuss new companions to the Bressoud even moduli identities. In particular, all 10 mod 20 identities are derived.

Cited by

• Further Applications of Cubic q-Binomial Transformations

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