International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 27-36
Summability methods based on the Riemann Zeta function
Department of Mathematics and Computer Science, State University Of North Dakota - Minot, Minot 58701, ND, USA
Received 12 September 1986
Copyright © 1988 Larry K. Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequence to be zeta summable. A zeta summability matrix associated with a real sequence is introduced; a necessary and sufficient condition on the sequence such that maps to is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated.