## \((1-q)(1-q^2)\dots(1-q^m)\) Revisited

#### When/Where:

October 31, 2017, 3:00 — 3:50 pm at LIT 368.

#### Abstract:

Let

\(\displaystyle (1-q)(1-q^2) … (1-q^m) = \sum_{n>= 0} c_m (n) q^n.\)

In this talk I discuss how to use \( q\)- binomial theorem together with the Euler pentagonal number theorem to show that \(\max( |c_m|) = 1\) iff \( m = 0,\ 1,\ 2,\ 3,\ 5\). There are many other similar results. For example, it can be proven that no positive integer m exists such that \(\max( |c_m|) = 9\).

This talk is based on my recent joint work with Ali Uncu (RISC, Linz).