An extension of a proof of the Ramanujan congruences for multipartitions
Holly Swisher
Recently Lachterman, Schayer, and Younger published a new,
elegant proof of the celebrated Ramanujan congruences for the
partition function p(n). Their proof uses classical theory of modular
forms as well as a beautiful result of Choie, Kohnen, and Ono. In
this talk, we will begin with an introduction to partition theory,
including its relationship to modular forms, and then give a method
for generalizing Lachterman, Schayer, and Younger’s proof to include
Ramanujan congruences for multipartition functions p_k(n) and
Ramanujan congruences for p(n) for some prime powers.