scholarly journals Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta-Function

2010 ◽  
Vol 2010 (1) ◽  
pp. 215416 ◽  
Author(s):  
SamirH Saker
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Distribution Of Zeros ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

scholarly journals Investigation of a Control Function Determining the Location of the Zeros as a Possible Proof of the Riemann Hypothesis.

2022 ◽  
Author(s):  
Miroslav Sukenik
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Riemann Hypothesis ◽  
Control Function ◽  
Distribution Of Zeros ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Zero Points

The article examines the control function in relation to the distribution of Zeros on thecritical line x = 0,5. To confirm this hypothesis, it will be necessary to perform a large number ofstatistical analyzes of the distribution of non-trivial zero points of the Riemann Zeta function.

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 .

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