Paper folding, theta functions and the circle method (Q1588916)

A reader wanting to know the relations between the folding of a strip of paper, the series \(\sum z^{-2^n}\), the Erdős-Turan theorem on polynomials, the elliptic theta functions, the partition function \(\prod_{n\geq 1} (1-x^n)^{-1}\), and the existence of a measure for which the denominators of the convergents of the paper folding continued fraction are orthogonal, will certainly enjoy very much this rich and interesting paper.