Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on $\zeta ''(s)$ and $\zeta '''(s)$


Author: C. Yalçin Yildirim
Journal: Proc. Amer. Math. Soc. 124 (1996), 2311-2314
MSC (1991): Primary 11M26
DOI: https://doi.org/10.1090/S0002-9939-96-03755-0
MathSciNet review: 1371146
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: There is only one pair of non-real zeros of $\zeta ''(s)$, and of $\zeta '''(s)$, in the left half-plane. The Riemann Hypothesis implies that $\zeta ''(s)$ and $\zeta '''(s)$ have no zeros in the strip $0 \leq \Re s < \frac 12 % $.


References [Enhancements On Off] (What's this?)

  • 1. T. M. Apostol, Formulas for higher derivatives of the Riemann zeta function, Math. Comp. 44 (1985), 223-232. MR 86c:11063
  • 2. N. Levinson and H. L. Montgomery, Zeros of derivatives of the Riemann zeta-function, Acta Math. 133 (1974), 49-65. MR 54:5135
  • 3. A. Speiser, Geometrisches zur Riemannschen zetafunktion, Math. Ann. 110 (1934), 514-521.
  • 4. R. Spira, Zero-free regions of $\zeta ^{(k)}(s)$ , J. London Math. Soc. 40 (1965), 677-682. MR 31:5849
  • 5. E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd ed., Oxford, 1986. MR 88c:11049
  • 6. C. Y. Yildirim, A note on $\zeta ''(s)$ and $\zeta '''(s)$, detailed version, manuscript available by e-mail.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11M26

Retrieve articles in all journals with MSC (1991): 11M26


Additional Information

C. Yalçin Yildirim
Affiliation: Department of Mathematics, Bilkent University, Ankara 06533, Turkey
Email: yalcin@fen.bilkent.edu.tr

DOI: https://doi.org/10.1090/S0002-9939-96-03755-0
Received by editor(s): November 30, 1994
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society