TBA

In this talk, I will present an application of modular form on a small part of the problem about the congruence properties of partition function. This is based on an Ono’s early paper. First, I give the definition of modular form, cusp form, and then mention the Serre’s theorem. Finally, I will prove the statement that for any arithmetic progression $r (mod t)$, there are infinitely many integers $N ≡ r (mod t)$ for which $p(N)$ is even. While the idea of mock modular form proves more stronger results, here we will only have a glimpse of one of the connections between modular form and combinatorics.