The leading root of the partial theta function

@inproceedings{Sokal2012TheLR,
  title={The leading root of the partial theta function},
  author={Alan D. Sokal},
  year={2012}
}
  • Alan D. Sokal
  • Published 2012
  • Mathematics, Physics
  • Abstract I study the leading root x 0 ( y ) of the partial theta function Θ 0 ( x , y ) = ∑ n = 0 ∞ 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… CONTINUE READING

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