We describe new zero-free regions for the derivatives $\zetak(s)$ of the Riemann zeta function, which take the form of vertical strips in the right half-plane. We show that the zeros located in the narrow complements of these zero-free regions are simple and exhibit vertical periodicities that enable one to give exact formulas for their number.
"Zeros of high derivatives of the Riemann zeta function." Rocky Mountain J. Math. 45 (3) 903 - 928, 2015. https://doi.org/10.1216/RMJ-2015-45-3-903