On Small Distances Between Ordinates of Zeros of ζ ( s ) and ζ ′ ( s )

@inproceedings{Garaev2006OnSD,
  title={On Small Distances Between Ordinates of Zeros of ζ ( s ) and ζ ′ ( s )},
  author={M. Z. Garaev and Cem Yalçın Yıldırım},
  year={2006}
}
In this paper s = σ + it will denote a complex variable, where σ and t are real, and T will denote a large parameter. The relations between the zeros of a function and the zeros of its derivatives have been the object of much study. The case of the Riemann zeta-function ζ(s) presents many puzzles beginning with the Riemann hypothesis (RH). Speiser [11] showed that RH is equivalent to ζ ′(s) having no zeros in 0 < σ < 2 . From Riemann’s original work (proofs for some parts of which were provided… CONTINUE READING