The leading root of the partial theta function

Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    I study the leading root x 0(y) of the partial theta function Θ0(x,y)=∑n=0∞xnyn(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.

    Original languageEnglish (US)
    Pages (from-to)2603-2621
    Number of pages19
    JournalAdvances in Mathematics
    Volume229
    Issue number5
    DOIs
    StatePublished - Mar 20 2012

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    Theta Functions
    Roots
    Partial
    Constant term
    Coefficient
    Strictly
    Formal Power Series
    Strictly positive

    Keywords

    • Formal power series
    • Implicit function theorem
    • Partial theta function
    • Q-Series
    • Rogers-Ramanujan function
    • Root

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    The leading root of the partial theta function. / Sokal, Alan D.

    In: Advances in Mathematics, Vol. 229, No. 5, 20.03.2012, p. 2603-2621.

    Research output: Contribution to journalArticle

    Sokal, Alan D. / The leading root of the partial theta function. In: Advances in Mathematics. 2012 ; Vol. 229, No. 5. pp. 2603-2621.
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