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International Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 1, Pages 27-36
http://dx.doi.org/10.1155/S0161171288000067

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 Hindawi Publishing Corporation. 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.

Abstract

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 x to be zeta summable. A zeta summability matrix Zt associated with a real sequence t is introduced; a necessary and sufficient condition on the sequence t such that Zt maps l1 to l1 is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated.