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.
Bibliographical noteFunding Information:
Haseo Ki was supported by Mid-career Researcher Program through NRF grant funded by the MEST 2010-0008706 .
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