Abstract
Every function holomorphic on a compact subset of the complex plane having connected complement can be approximated by translates of Taylor polynomials of the Riemann zeta function.
Similar content being viewed by others
References
B. Bagchi, A joint universality Theorem for Dirichlet L-functions, Math. Zeit. 181 (1982), 319–335.
C. K. Chui and M. N. Parnes, Approximation by overconvergence of a power series, J. Math. Anal. Appl. 36 (1971), 693–696.
K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.) 36 (1999), 345–381.
P. M. Gauthier and N. Tarkhanov, Approximation by the Riemann zeta-function, Complex Variables, Theory Appl. 50 (2005), 211–215.
W. Luh, Approximation analytischer Funktionen durch überkonvergente Potenzreihen und deren Matrix-Transformierten, Mitt. Math. Sem. Gießen 88 (1970), 1–56.
W. Luh, Uber den Satz von Mergelyan, J. Approx. Theory 16 (1976), 194–198.
A. Melas, V. Nestoridis and I. Papadoperakis, Growth of coefficients of universal Taylor series and comparison of two classes of functions, J. Anal. Math. 73 (1997), 187–202.
V. Nestoridis, Universal Taylor series, Ann. Inst. Fourier 46 (1996), 1293–1306.
J. Steuding, Value Distribution of L-Functions, Lecture Notes in Mathematics 1877, Springer, New York, 2005.
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported by NSERC (Canada).
Rights and permissions
About this article
Cite this article
Gauthier, P.M., Clouâtre, R. Approximation by Translates of Taylor Polynomials of the Riemann Zeta Function. Comput. Methods Funct. Theory 8, 15–19 (2008). https://doi.org/10.1007/BF03321666
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03321666