Number Theory Seminar

Steve Gonek, University of Rochester

The Density of the Riemann Zeta Function on the Critical Line

K. Ramachandra asked whether the curve f(t)=\zeta(1/2+it), t \in \R, is dense in the complex plane. We show that if the Riemann hypothesis, a zero-spacing hypothesis, and a plausible assumption about the uniform distribution modulo one of the normalized ordinates of the zeros of the zeta function hold, then the answer is yes.

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