Global and local behavior of zeros of nonpositive type

A generalized Nevanlinna function $Q(z)$ with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation defined by $Q_τ(z)=(Q(z)-τ)/(1+τQ(z))$, $τ\in \mathbf{Real} \cup \{\infty\}$, is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type $α(τ)$ as a function of $τ$ is being studied. In particular, it is shown that it is continuous and its behavior in the points where the function extends through the real line is investigated.

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