The Ramanujan-Dyson identities and George Beck’s Congruence Conjectures

When/Where:

March 19, 2019, 3:00 — 3:50 pm at LIT 368.

Abstract:

Dyson’s famous conjectures (proved by Atkin and Swinnerton-Dyer) give a combinatorial interpretation of Ramanujan’s congruences for the partition function. The proofs of these conjectures center on the universal mock theta function associated with the rank of a partition. George Beck has generalized the study of partition function congruences related to the rank by considering the total number of parts in the partitions of n. The related generating functions are no longer part of the world of mock theta functions.

However, George Beck has conjectured that certain linear combinations of the related enumerating functions do satisfy congruences modulo 5 and 7.

We shall describe the proofs of these conjectures.