Asymptotics of the fourth power moment of the Riemann zeta-function in the critical strip

1996 ◽  
Vol 36 (1) ◽  
pp. 32-44
Author(s):  
A. Kačènas
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Fourth Power ◽  
Critical Strip ◽  
Power Moment ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

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 SELF-APPROXIMATION FOR THE RIEMANN ZETA FUNCTION

2012 ◽  
Vol 87 (3) ◽  
pp. 452-461 ◽  
Author(s):  
TAKASHI NAKAMURA ◽  
ŁUKASZ PAŃKOWSKI
Keyword(s):  
Zeta Function ◽  
Half Plane ◽  
Riemann Zeta Function ◽  
Critical Strip ◽  
Approximation Of Functions ◽  
Joint Universality ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
The Right

AbstractIn the paper we deal with self-approximation of the Riemann zeta function in the half plane $\operatorname {Re} s\gt 1$ and in the right half of the critical strip. We also prove some results concerning joint universality and joint value approximation of functions $\zeta (s+\lambda +id\tau )$ and $\zeta (s+i\tau )$.

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