Ramanujan's congruences modulo powers of 5, 7, and 11 revisited
Sprache des Vortragstitels:
81st Séminaire Lotharingien de combinatoire
Sprache des Tagungstitel:
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.
Sprache der Kurzfassung:
Hauptvortrag / Eingeladener Vortrag auf einer Tagung