Self-intersections of the Riemann zeta function on the critical line

  title={Self-intersections of the Riemann zeta function on the critical line},
  author={William D. Banks and Victor Castillo-Garate and Luigi Fontana and Carlo Morpurgo},
  journal={Journal of Mathematical Analysis and Applications},
Abstract We show that the Riemann zeta function ζ has only countably many self-intersections on the critical line, i.e., for all but countably many z ∈ C the equation ζ ( 1 2 + i t ) = z has at most one solution t ∈ R . More generally, we prove that if F is analytic in a complex neighborhood of R and locally injective on R , then either the set { ( a , b ) ∈ R 2 : a ≠ b  and  F ( a ) = F ( b ) } is countable, or the image F ( R ) is a loop in C . 
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Meinen Dank für die Auszeichnung, welche mir die Akademie durch die Aufnahme unter ihre Correspondenten hat zu Theil werden lassen, glaube ich am besten dadurch zu erkennen zu geben, dass ich von der
Certain properties of analytic curves. II
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