### Newman's conjecture for the partition functions modulo composite numbers

Heilbronn Number Theory Seminar

3rd May 2023, 4:00 pm – 5:00 pm

Fry Building, 2.04

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.

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