Andrews, Ramanujan, and Computer Algebra

Description

The red thread of the talk is made from various mathematical ideas which, to my pleasure, George Andrews was sharing with me already in statu nascendi. The first part of the talk is devoted to aspects of partition analysis, invented by MacMahon more than hundreds of years ago, and brought back to the stage by Andrews. Partition analysis is a method to deal with systems of linear Diophantine constraints over the nonnegative integers and thus providing connections to many areas in discrete mathematics, including discrete geometry. Computer algebra experiments carried out with Omega, a computer algebra package implemented by Axel Riese in cooperation with Andrews and the speaker, led to a new combinatorial construction of quotients of Dedekind eta functions. This work in turn stimulated new algorithmic developments by Silviu Radu to manipulate modular forms and functions, and to prove related congruences arising in additive number theory. The talk gives a general overview with numerous examples, many of them related, directly or indirectly, to Srinivasa Ramanujan.

Period	17 Mar 2014
Event title	unbekannt/unknown
Event type	Other
Location	AustriaShow on map