Where do the maximum absolute $q$-series coefficients of $(1-q)(1-q^2)(1-q^3)\dots(1-q^{n-1})(1-q^n)$ occur?

Alexander Berkovich; Ali K. Uncu

paper

Where do the maximum absolute $q$ -series coefficients of $(1 - q) (1 - q^{2}) (1 - q^{3}) \dots (1 - q^{n - 1}) (1 - q^{n})$ occur?

arXiv:1911.03707

Abstract

We used the MACH2 supercomputer to study coefficients in the $q$ -series expansion of $(1 - q) (1 - q^{2}) \dots (1 - q^{n})$ , for all $n \leq 75000$ . As a result, we were able to conjecture some periodic properties associated with the before unknown location of the maximum coefficient of these polynomials with odd $n$ . Remarkably the observed period is 62,624.

9 pages, 1 figure, 3 tables

Cited by in corpus (1)

Errata and Addenda to Mathematical Constants

Where do the maximum absolute q-series coefficients of (1−q)(1−q2)(1−q3)…(1−qn−1)(1−qn) occur?

Abstract

Cited by in corpus (1)

Where do the maximum absolute $q$ -series coefficients of $(1 - q) (1 - q^{2}) (1 - q^{3}) \dots (1 - q^{n - 1}) (1 - q^{n})$ occur?