Analytic properties of the partial theta function

Abstract: We consider the partial theta function $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$, where $x$ is a variable and $q$ a parameter ($|q|<1$). We deal with the two possible situations, when $q$ is real or complex. In the talk we focus on the analytic properties of $\theta$, such as asymptotic expansions for its zeros, its spectrum (i.e. the set of values of the parameter $q$ for which $\theta (q,.)$ has multiple zeros), behaviour of its zeros, especially of its complex conjugate pairs, when the parameter $q$ varies, separation in modulus of the zeros etc.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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