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