On the q-binomial identities involving the Legendre symbol modulo 3

2023/02/12 by Alexander Bérkovich, Berkovich, Alexander
Chemistry · Mathematics · #05A10 #05A15 #05A17} #11P81 #11P82 #11P83 #11P84 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT) #Secondary 11C08 #{Primary 11B65

paper · pdf · doi:10.48550/arxiv.2302.06017

openalex publication_date 2023/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I use polynomial analogue of the Jacobi triple product identity together with the Eisenstein formula for the Legendre symbol modulo 3 . to prove six identities involving the q-binomial coefficients. These identities are then extended to the new infinite hierarchies of q-series identities by means of the special case of Bailey's lemma. Some of the identities of Ramanujan, Slater, McLaughlin and Sills are obtained this way.

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