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

Alexander Berkovich

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arXiv · 2302.06017

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

Alexander Berkovich

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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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Alexander Berkovich. 2023-02-12. On the q-binomial identities involving the Legendre symbol modulo 3. https://arxiv.org/abs/2302.06017

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