Hostname: page-component-cb9f654ff-lqqdg Total loading time: 0 Render date: 2025-08-25T04:28:34.128Z Has data issue: false hasContentIssue false
  • English
  • Français

Value Distribution of the Riemann Zeta Function

Published online by Cambridge University Press:  20 November 2018

I. Ascah-Coallier  and
P. M. Gauthier
I. Ascah-Coallier
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, Montréal, QC H3C 3J7. e-mail: ascahc@dms.umontreal.ca, e-mail: gauthier@dms.umontreal.ca
P. M. Gauthier
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, Montréal, QC H3C 3J7. e-mail: ascahc@dms.umontreal.ca, e-mail: gauthier@dms.umontreal.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note, we give a new short proof of the fact, recently discovered by Ye, that all (finite) values are equidistributed by the Riemann zeta function.

Keywords

30D35Nevanlinna theorydeficiencyRiemann zeta function

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 3 , 01 September 2008 , pp. 334 - 336
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Berndt, B. C., The number of zeros for ζ(k)(s), J. Lond. Math. Soc. 2(1970), 577–580.Google Scholar
[2] Liao, L. and Yang, C-C., On some new properties of the gamma function and the Riemann zeta function. Math. Nachr. 257(2003), 59–66.Google Scholar
[3] Liao, L. and Ye, Zhuan, The Lang-type of the Riemann zeta-function. Complex Var. Elliptic Equ. 51(2006), no. 3, 239–241.Google Scholar
[4] Nevanlinna, R., Analytic Functions. Translated from the second German edition. Die Grundlehren der mathematischen Wissenschaften 162, Springer-Verlag, New York, 1970.Google Scholar
[5] Verma, D. P. and Kaur, A., Zero-free regions of derivatives of Riemann zeta function. Proc. Indian Acad. Sci., Math. Sci. 91(1982), no. 3, 217–221.Google Scholar
[6] Ye, Z., The Nevanlinna functions of the Riemann zeta-function. J. Math. Anal. Appl. 233(1999), no. 1, 425–435.Google Scholar