Rocky Mountain Journal of Mathematics

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

Jeffrey Stopple

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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

Permanent link to this document
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

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$ 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72} 11M50: Relations with random matrices

Keywords
Riemann zeta function logarithmic derivative

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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