Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines

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