Ramanujan's congruences modulo powers of 5, 7, and 11 revisited

Description

In 1919 Ramanujan conjectured three infinite families of congruences for the partition function modulo powers of 5, 7, and 11. In 1938 Watson proved the 5-case and (a corrected version of) the 7-case. In 1967 Atkin proved the remaining 11-family using a method significantly different from Watson's. In joint work with Silviu Radu (RISC) we set up a new algorithmic framework which brings all these cases under one umbrella. In this talk I will report on various new aspects of this setting. One aspect concerns a statement of Atkin who remarked that, in comparison with the 5 and 7-case, his proof for 11 is "indeed 'langweilig', as Watson suggested". In our framework we find the 11-case particularly interesting.

Period	10 Sept 2018
Event title	81st Séminaire Lotharingien de combinatoire
Event type	Conference
Location	AustriaShow on map