Landau-Siegel zeros and zeros of the derivative of the Riemann zeta function

David W. Farmer, Haseo Ki

Published 2010-02-08Version 1

We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.