scholarly journals Dynamical Zeta Function for Several Strictly Convex Obstacles

2008 ◽  
Vol 51 (1) ◽  
pp. 100-113 ◽  
Author(s):  
Vesselin Petkov
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Absolute Convergence ◽  
Strictly Convex ◽  
Dynamical Zeta Function ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Analytic Singularities

AbstractThe behavior of the dynamical zeta function ZD(s) related to several strictly convex disjoint obstacles is similar to that of the inverse Q(s) = of the Riemann zeta function ζ(s). Let Π(s) be the series obtained from ZD(s) summing only over primitive periodic rays. In this paper we examine the analytic singularities of ZD(s) and Π(s) close to the line , where s2 is the abscissa of absolute convergence of the series obtained by the second iterations of the primitive periodic rays. We show that at least one of the functions ZD(s), Π(s) has a singularity at s = s2.

scholarly journals On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
WonTae Hwang ◽  
Kyunghwan Song
Keyword(s):  
Zeta Function ◽  
Rational Number ◽  
Riemann Zeta Function ◽  
Rational Numbers ◽  
Critical Strip ◽  
Integer Part ◽  
Integral Points ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

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 .

scholarly journals On The Tails of the Exponential Series

1994 ◽  
Vol 37 (2) ◽  
pp. 278-286 ◽  
Author(s):  
C. Yalçin Yildirim
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Partial Sums ◽  
Maclaurin Series ◽  
Exponential Series ◽  
Asymptotic Estimation ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

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.

On the Riemann zeta-function

1932 ◽  
Vol 28 (3) ◽  
pp. 273-274 ◽  
Author(s):  
E. C. Titchmarsh
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Absolute Constant ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Image Position

It was proved by Littlewood that, for every large positive T, ζ (s) has a zero β + iγ satisfyingwhere A is an absolute constant.

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