Functiones et Approximatio Commentarii Mathematici

Zeros of the derivatives of the Riemann zeta-function

Haseo Ki and Yoonbok Lee

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Abstract

Levinson and Montgomery in 1974 proved many interesting formulae on the zeros of derivatives of the Riemann zeta function $\zeta(s)$. When Conrey proved that at least 2/5 of the zeros of the Riemann zeta function are on the critical line, he proved the asymptotic formula for the mean square of $\zeta(s)$ multiplied by a mollifier of length $ T^{4/7}$ near the $1/2$-line. As a consequence of their papers, we study some aspects of zeros of the derivatives of the Riemann zeta function with no assumption.

Article information

Source
Funct. Approx. Comment. Math., Volume 47, Number 1 (2012), 79-87.

Dates
First available in Project Euclid: 25 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.facm/1348578278

Digital Object Identifier
doi:10.7169/facm/2012.47.1.7

Mathematical Reviews number (MathSciNet)
MR2987112

Zentralblatt MATH identifier
1312.11068

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

Keywords
zeros derivatives Riemann zeta function.

Citation

Ki, Haseo; Lee, Yoonbok. Zeros of the derivatives of the Riemann zeta-function. Funct. Approx. Comment. Math. 47 (2012), no. 1, 79--87. doi:10.7169/facm/2012.47.1.7. https://projecteuclid.org/euclid.facm/1348578278


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References

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