Abstract
For an arbitrary complex number ane 0 we consider the distribution of values of the Riemann zeta-function zeta at the a-points of the function Delta which appears in the functional equation zeta (s)=Delta (s)zeta (1-s). These a-points delta _a are clustered around the critical line 1/2+imathbb {R} which happens to be a Julia line for the essential singularity of zeta at infinity. We observe a remarkable average behaviour for the sequence of values zeta (delta _a).
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