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Summability methods based on the Riemann Zeta function

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  • Larry K. Chu

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 Z t associated with a real sequence t is introduced; a necessary and sufficient condition on the sequence t such that Z t maps l 1 to l 1 is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated.

Suggested Citation

  • Larry K. Chu, 1988. "Summability methods based on the Riemann Zeta function," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:765609
    DOI: 10.1155/S0161171288000067
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