Ramanujan's classic congruence families were the first important arithmetic properties that were discovered for the partition function p(n); prior to their discovery, it was believed 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, possible connections to the subject of Galois representations, and the implications for future work on the most difficult problems in the subject.
Partitions and Congruence Ideals
30.01.2024 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: