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 -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.
Keywords
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}
}
Comments
8 paages