Peter Paule

Affiliation: RISC, J. Kepler University, Linz

Email: Peter.Paule@risc.uni-linz.ac.at

Title Of Talk: Alladi, Goellnitz-Gordon, and Computer Algebra

Abstract: As a by-product of his recent work on partitions with non-repeating odd parts, Krishna Alladi derived an elegant modular relation in a natural combinatorial setting. Analytically this relation states the equality of an eta-quotient with $G(-q^2)-q H(-q^2)$, where $G(q)$ and $H(q)$ are the functions describing the Goellnitz-Gordon partitions. Taking this identity as a starting point, the talk describes recent algorithmic developments in connection with modular functions. A major general tool emerged from Radu's work on his Ramanujan-Kolberg package, namely a computer algebra algorithm to compute suitable presentations of subalgebras. Applications related to modular functions concern computer-assisted proving and discovery of $q$-series and $q$-product identities. Finally, along with a new proof of Alladi's modular relation, further possible algorithmic developments are discussed. The material of this talk arose in joint work with Silviu Radu.