Rogers-Ramanujan-Slater Type Identities

By J. Laughlin, Andrew V. Sills, Peter Zimmer. 2008

65 citations recorded by the source corpus.

In this survey article, we present an expanded version of Lucy Slater’s famous list of identities of the Rogers-Ramanujan type, including identities of similar type, which were discovered after the publication of Slater’s papers, and older identities (such as those in Ramanujan’s lost notebook) which were not included in Slater’s papers. We attempt to supply the earliest known reference for each identity. Also included are identities of false theta functions, along with their relationship to RogersRamanujan type identities. We also describe several ways in which pairs/larger sets of identities may be related, as well as dependence relationships between identities.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/18e71570ee4790751cc9aa1ef760f8ee80ed522b

Citations in the corpus

• Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial (2011, unknown): “By the Jacobi triple product identity f(a;b) can be expressed as: f(a;b) = ( a;ab) 1( b;ab) 1(ab;ab) 1: In particular f( q2; q) = (q;q) 1. Note that f(a;b) = f(b;a): (2)The false theta function (e.g. [MSZ08]): (a;b) := X1 k=0 ak(k+1)=2bk(k 1)=2 X1 k=1 ak(k 1)=2bk(k+1)=2 Note that (a;b) 2 = (b;a): 2.”
• The head and tail conjecture for alternating knots (2011, unknown): “[16]): Ψ(a, b) := ∞ ∑”