On the a-points of derivatives of the Riemann zeta function

Abstract

We prove three results on the a-points of derivatives of the Riemann zeta function. The first result is a formula of the Riemann–von Mangoldt type; we estimate the number of a-points of derivatives of the Riemann zeta function. The second result is on certain exponential sum involving a-points. The third result is an analogue of the zero density theorem. We count the a-points of derivatives of the Riemann zeta function in \(1/2-(\log \log T)^2/\log T<\mathrm{Re}\, s<1/2+(\log \log T)^2/\log T\).