Number Theory


The Zeros of the Hardy Z Function are Simple

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.

Comments: 3 Pages.

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Submission history

[v1] 2017-02-26 23:55:26
[v2] 2017-02-27 13:42:01

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