797 research outputs found
Dedekind's eta-function and Rogers-Ramanujan identities
We prove a q-series identity that generalises Macdonald's A_{2n}^{(2)}
eta-function identity and the Rogers-Ramanujan identities. We conjecture our
result to generalise even further to also include the Andrews-Gordon
identities.Comment: 14 page
Some new series for and related congruences
In this paper we prove some new series for as well as related
congruences. We also raise several new kinds of series for and present
some related conjectural congruences involving representations of primes by
binary quadratic forms.Comment: 16 pages, published versio
Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
We compute the one-dimensional configuration sums of the ABF model using the
fermionic technique introduced in part I of this paper. Combined with the
results of Andrews, Baxter and Forrester, we find proof of polynomial
identities for finitizations of the Virasoro characters
as conjectured by Melzer. In the thermodynamic limit
these identities reproduce Rogers--Ramanujan type identities for the unitary
minimal Virasoro characters, conjectured by the Stony Brook group. We also
present a list of additional Virasoro character identities which follow from
our proof of Melzer's identities and application of Bailey's lemma.Comment: 28 pages, Latex, 7 Postscript figure
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