# Alexander Berkovich

## $$(1-q)(1-q^2)\dots(1-q^m)$$ 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).