Authors: Stephen Crowley
It is proved that the non-trivial roots of the Hardy Z function are simple having multiplicity 1 by showing that the fixed-points N_Z(α)=α of the Newton map N_Z(t)=t-(Z(t))/(Z˙(t)) must have a multiplier λ_(N_Z)(α)=|(N_Z)˙(α)|=|(Z(α)Z¨(α))/(Z˙(α))|=0 and therefore a multiplicity m_Z(α)=1/(1-λ_(N_Z)(α))=1/(1-0)=1.
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