Abstract
The question of the horizontal distribution of the zeros of derivatives of Riemann’s zeta-function is an interesting one in view of its connection with the Riemann Hypothesis.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. B. Conrey, Zeros of derivatives of Riemann’s xi-function on the critical line, J. Number Th. 16 (1983), 49–74.
J. B. Conrey, The fourth moment of derivatives of the Riemann zeta-function, Quart. J. Math. Oxford (2) 39 (1988), 21–36.
J. B. Conrey and A. Ghosh, A mean value theorem for the Riemann zeta-function at its relative extrema on the critical line, J. London Math. Soc. (2) 32 (1985), 193–202.
J. B. Conrey and A. Ghosh, On the zeros of the Taylor polynomials associated with the exponential function, American Math. Monthly 95 (1988), 528–533.
S. M. Gonek, Mean values of the Riemann zeta-function and its derivatives, Invent. Math. 75 (1984), 123–141.
N. Levinson, More than one-third of zeros of Riemann’s zeta-function are on σ = 1/2, Adv. in Math. 13 (1974), 383–436.
N. Levinson and H. L. Montgomery, Zeros of the derivatives of the Riemann zeta-function, Acta Math. 133 (1974), 49–65.
A. Selberg, On the zeros of Riemann’s zeta-function, Skr. Norske Vid. Akad. Oslo 10 (1942), 1–59.
A. Speiser, Geometrisches zur Riemannschen Zetafunktion, Math. Ann. 110 (1934), 514–521.
R. Spira, Zero-free regions of ζ′ (k) (s)J. London Math Soc. 40 (1965), 677–682.
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford University Press, 1951.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
To Paul Bateman on the occasion of his seventieth birthday
Rights and permissions
Copyright information
© 1990 Bikhäuser Boston
About this chapter
Cite this chapter
Conrey, J.B., Ghosh, A. (1990). Zeros of Derivatives Of the Riemann Zeta-Function Near the Critical Line. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds) Analytic Number Theory. Progress in Mathematics, vol 85. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3464-7_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3464-7_8
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3481-0
Online ISBN: 978-1-4612-3464-7
eBook Packages: Springer Book Archive