Duke Mathematical Journal

On the zeros of $\zeta'(s)$ near the critical line

Yitang Zhang

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Abstract

Let $\rho^\prime=\beta^\prime+i\gamma^\prime$ denote the zeros of $\zeta^\prime(s),s=\sigma+it$. It is shown that there is a positive proportion of the zeros of $\zeta^\prime(s)$ in $0<t<T$ satisfying $\beta^\prime-1/2\ll(\log T)^{-1}$. Further results relying on the Riemann hypothesis and conjectures on the gaps between the zeros of $\zeta(s)$ are also obtained.

Article information

Source
Duke Math. J. Volume 110, Number 3 (2001), 555-572.

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1087574981

Digital Object Identifier
doi:10.1215/S0012-7094-01-11034-X

Mathematical Reviews number (MathSciNet)
MR1869116

Zentralblatt MATH identifier
1012.11081

Subjects
Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Citation

Zhang, Yitang. On the zeros of $\zeta'(s)$ near the critical line. Duke Math. J. 110 (2001), no. 3, 555--572. doi:10.1215/S0012-7094-01-11034-X. http://projecteuclid.org/euclid.dmj/1087574981.


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