2007/06/01 by Andrew V. Sills · 28 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebra over a field #Analytic Number Theory Research #Combinatorics #Mathematics #Pure mathematics #Ramanujan tau function #Ramanujan theta function #Ramanujan's sum #Type (biology) #math.NT #msc:05A19 #msc:11B65 #msc:11P81 #msc:39A13
paper · pdf · doi:10.1142/s1793042107000912
published in International Journal of Number Theory 03(02), 293-323 (World Scientific) · 28 pages
openalex publication_date 2007/06/01 · arxiv created 2018/12/13 · arxiv updated 2018/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers–Ramanujan identities (L. J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math Soc. (2)54 (1952) 147–167) can be easily derived using just three multiparameter Bailey pairs and their associated q-difference equations. As a bonus, new Rogers–Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.