Youngmin Lee

Newman's conjecture for the partition functions modulo composite numbers

For a positive integer n, let p(n) be the number of partitions of n. In 1960, Newman conjectured that for any integers M and r with r < M and non-negative, there are infinitely many positive integers n such that p(n) is congruent to r modulo M. In this talk, we will explain our results related to Newman's conjecture. Moreover, we will introduce an analogue of Newman's conjecture for the Fourier coefficients of a weakly holomorphic modular form and its applications such as the congruence properties for the number of t-core partitions. This work is joint with Dohoon Choi.