Seminars and Colloquia
Mathematics
Results on zeros of combinations of derivatives of completed Riemann zeta function
Tue, Feb 27, 2018,
04:00 PM to 05:00 PM
at Madhava Hall
Dr. Sneha Chaubey
Goettingen
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 100 percent as the order of the derivative increases. In this talk, we prove a result for combinations of derivatives of ξ(s). Although our combinations do not always have all their zeros on the critical line, we show that the proportion of zeros on the critical line tends to 1.
