Value Distribution of the Riemann Zeta Function
Canadian mathematical bulletin, Tome 51 (2008) no. 3, pp. 334-336

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2008-033-0
Mots-clés : 30D35, Nevanlinna theory, deficiency, Riemann zeta function
Ascah-Coallier, I.; Gauthier, P. M. Value Distribution of the Riemann Zeta Function. Canadian mathematical bulletin, Tome 51 (2008) no. 3, pp. 334-336. doi: 10.4153/CMB-2008-033-0
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[1] [1] Berndt, B. C., The number of zeros for ζ(k)(s), J. Lond. Math. Soc. 2(1970), 577–580. Google Scholar

[2] [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] [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] [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] [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] [6] Ye, Z., The Nevanlinna functions of the Riemann zeta-function. J. Math. Anal. Appl. 233(1999), no. 1, 425–435. Google Scholar

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