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.