Zeros of nonpositive type of generalized Nevanlinna functions with one negative square

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 + τ Q ( z ) ) , τ ∈ R ∪ { ∞ } , is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type α ( τ ) as a function of τ defines a path in the closed upper halfplane. Various properties of this path are studied in detail.