Abstract:
Ramanujan's classic congruence families were the first important arithmetic properties that were discovered for the partition function p(n); prior to their discovery, we had assumed that the arithmetic of p(n) was effectively pseudorandom. Over the last century we have discovered a very broad class of other congruence families exhibited by the coefficients of various other modular forms. These families superficially resemble those of p(n), but they are often much more difficult to prove. In this talk we give an example of a more recently discovered congruence family, the difficulties involved in proving it, some remarkable internal algebraic structures that emerge along the way, and the implications for future work.
Partitions, Congruence Ideals, and the Localization Method
24.10.2023 15:15 - 16:45
Organiser:
I. Fischer, M. Schlosser
Location: