Geometry Seminar - Abstracts


Wednesday 14 November 2018, 14:00-15:00 in HG03.085
Alex Berkovich (Gainesville, Florida)
Sudler's products revisited


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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