## Rocky Mountain Journal of Mathematics

### Notes on $\log (\zeta (s))^\prime \prime$

Jeffrey Stopple

#### Abstract

Motivated by the connection to the pair correlation of the Riemann zeros, we investigate the second derivative of the logarithm of the Riemann $\zeta$ function, in particular, the zeros of this function. Theorem~1.2 gives a zero-free region. Theorem~1.4 gives an asymptotic estimate for the number of nontrivial zeros to height $T$. Theorem~1.7 is a zero density estimate.

#### Article information

Source
Rocky Mountain J. Math., Volume 46, Number 5 (2016), 1701-1715.

Dates
First available in Project Euclid: 7 December 2016

https://projecteuclid.org/euclid.rmjm/1481101232

Digital Object Identifier
doi:10.1216/RMJ-2016-46-5-1701

Mathematical Reviews number (MathSciNet)
MR3580807

Zentralblatt MATH identifier
1215.11085

#### Citation

Stopple, Jeffrey. Notes on $\log (\zeta (s))^\prime \prime$. Rocky Mountain J. Math. 46 (2016), no. 5, 1701--1715. doi:10.1216/RMJ-2016-46-5-1701. https://projecteuclid.org/euclid.rmjm/1481101232

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