scholarly journals Summability methods based on the Riemann Zeta function

Author(s):  
Larry K. Chu

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 sequencexto be zeta summable. A zeta summability matrixZtassociated with a real sequencetis introduced; a necessary and sufficient condition on the sequencetsuch thatZtmapsl1tol1is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated.

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
WonTae Hwang ◽  
Kyunghwan Song

Abstract We prove that the integer part of the reciprocal of the tail of $\zeta (s)$ ζ ( s ) at a rational number $s=\frac{1}{p}$ s = 1 p for any integer with $p \geq 5$ p ≥ 5 or $s=\frac{2}{p}$ s = 2 p for any odd integer with $p \geq 5$ p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p}$ s = 2 p , we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$ Q .


1994 ◽  
Vol 37 (2) ◽  
pp. 278-286 ◽  
Author(s):  
C. Yalçin Yildirim

AbstractA relation between the zeros of the partial sums and the zeros of the corresponding tails of the Maclaurin series for ez is established. This allows an asymptotic estimation of a quantity which came up in the theory of the Riemann zeta-function. Some new properties of the tails of ez are also provided.


Sign in / Sign up

Export Citation Format

Share Document