International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 27-36
doi:10.1155/S0161171288000067

Summability methods based on the Riemann zeta function

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.