Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T02:39:09.635Z Has data issue: false hasContentIssue false
  • English
  • Français

Universally Overconvergent Power Series via the Riemann Zeta-function

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier
P. M. Gauthier*
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, CP-6128 Centreville, Montréal, QC, H3C 3J7 e-mail: [email protected]
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.

The Riemann zeta-function is employed to generate universally overconvergent power series.

Keywords

30K0511M06overconvergencezeta-function
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 544 - 550
Copyright
Copyright © Canadian Mathematical Society 2013

References

[1] Bohr, H., Zur Theorie der Riemannschen Zetafunktion im kritischen Streifen. Acta. Math. 40 (1915, 67–100.Google Scholar
[2] Clouâtre, R., Universal power series in CN: Canad. Math. Bull. 54 (2011, no. 2, 230–236.Google Scholar
[3] Chui, C. K. and Parnes, M. N., Approximation by overconvergence of a power series. J. Math. Anal. Appl. 36 (1971, 693–696. http://dx.doi.org/10.1016/0022-247X(71)90049-7 Google Scholar
[4] Grosse-Erdmann, K.-G., Holomorphe Monster und universelle Funktionen. Mitt. Math. Sem. Giessen 176 (1987.Google Scholar
[5] Grosse-Erdmann, K.-G., Universal families and hypercyclic operators. Bull. Am. Math. Soc. (N. S.) 36 (1999, no. 3, 345–381. http://dx.doi.org/10.1090/S0273-0979-99-00788-0 Google Scholar
[6] Luh, W., Approximation analytischer Funktionen durch überkonvergente Potenzreihen und deren Matrix-Transformierten. Mitt. Math. Semin. Giessen 88 (1970.Google Scholar
[7] Nestoridis, V., Universal Taylor series. Ann. Inst. Fourier 46 (1996, no. 5, 1293–1306. http://dx.doi.org/10.5802/aif.1549 Google Scholar
[8] Poirier, A., Séries universelles construites `a l’aide de la fonction zeta de Riemann. In: Progress in Analysis and its Applications, Proceedings of the 7th ISAAC Congress,World Scientific Publishing CSingapore, o., 2010, pp. 164–170,Google Scholar
[9] Reich, A., Wertverteilung von Zetafunktionen. Arch. Math. (Basel) 34 (1980, 440–451.Google Scholar
[10] Selesnev, A. I., On universal power series. (Russian) Mat. Sbornik N.S. 28 (70(1951), 453–460.Google Scholar
[11] Voronin, S. M., On the distribution of nonzero values of the Riemann ζ-function. Proc. Steklov Inst. Math. 128 (1972, 153–175; translation from Trudy Mat. Inst. Steklov 128 (1972, 131–150.Google Scholar