## Geometry Seminar - Abstracts

### Talk

Wednesday 14 November 2018, 14:00-15:00 in HG03.085

**Alex Berkovich** (Gainesville, Florida)

*Sudler's products revisited*

### Abstract

Let \((1-q)(1-q^2)\cdots(1-q^m) = \sum_{n\ge0} c_m(n)q^n\).
In this talk I discuss how to use \(q\)-binomial theorem together with the Euler
pentagonal number theorem to show that
\(\max_{n\ge0}|c_m(n)|=1\) 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 \(\max_{n\ge0}|c_m(n)|=9\).
The talk is based on a joint work with Ali K. Uncu (RISC, Linz, Austria).

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