Скачать или смотреть Sneha Chaubey - Combinations of derivatives of Riemann-Xi function

Proportion of zeros of combinations of derivatives of Riemann-Xi function on the critical line

Speaker: Sneha Chaubey
University of Illinois

The talk was given at the number theory seminar on November 24th, 2016 (Department of Pure Mathematics, University of Waterloo)

Abstract:
The Riemann Hypothesis implies that the zeros of all the derivatives of the Riemann-Xi function (ξ(s)) lie on the critical line. Results on the proportion of zeros on the critical line of derivatives of ξ(s) have been investigated before, and it has been shown, that the percentage of zeros of ξ(k)(s) approaches a 100 percent as the order of the derivative increases. In this talk, we prove a result for combinations of derivatives of ξ(s). Although not always our combinations have all their zeros on the critical line, we show that the proportion of zeros on the critical line tends to 1.