1106.1003 (Alan D. Sokal)

The leading root of the partial theta function    [PDF]

Alan D. Sokal

I study the leading root x_0(y) of the partial theta function \Theta_0(x,y) =
\sum_{n=0}^\infty x^n y^{n(n-1)/2}, considered as a formal power series. I
prove that all the coefficients of -x_0(y) are strictly positive. Indeed, I
prove the stronger results that all the coefficients of -1/x_0(y) after the
constant term 1 are strictly negative, and all the coefficients of 1/x_0(y)^2
after the constant term 1 are strictly negative except for the vanishing
coefficient of y^3.

View original: http://arxiv.org/abs/1106.1003