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Number Theory Seminar

On the zeros of derivatives (and their combinations) of the completed Riemann zeta function

Amita Malik

Location:  Hill 425
Date & time: Tuesday, 05 December 2017 at 2:00PM - 3:00PM

It is known that the Riemann Hypothesis for the completed Riemann zeta function  \(xi(s)\) implies the Riemann Hypothesis for its higher derivatives. Conrey investigated the proportion of zeros of higher derivatives on the critical line and proved that this proportion approaches 1 as the order of the derivative becomes large. On the other hand, vertical distribution of zeros of the Riemann zeta function has also attracted a lot of attention. In this talk, we discuss the distribution of imaginary parts of zeros of derivatives of \(xi(s)\), and the proportion of zeros of combinations of these derivatives on the critical line.