Invited colloquium talk at Montanuniversität Leoben
Sprache des Tagungstitel:
The Rogers-Ramanujan identities are two celebrated identities in number theory. They have manifold facets ranging from aspects of enumerative combinatorics and special functions, to their appearance in Baxter's solution of the hard hexagon model in statistical mechanics. Combinatorially the first Rogers-Ramanujan function can be defined as the generating function of the number of integer partitions in which the differences between parts are at least two. The second Rogers-Ramanujan function is defined similarly. The talk discusses various aspects of these functions in the light of recent computer algebra developments. Topics include modular functions, the Rogers-Ramanujan continued fraction, and its connection to Felix Klein's icosahedral equation.