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

Number Theory 2023-02-14 v1

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 qq-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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Cite

@article{arxiv.2302.06017,
  title  = {On the q-binomial identities involving the Legendre symbol modulo 3},
  author = {Alexander Berkovich},
  journal= {arXiv preprint arXiv:2302.06017},
  year   = {2023}
}

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