scholarly journals A Multidimensional Hilbert-Type Integral Inequality Related to the Riemann Zeta Function

2014 ◽  
pp. 417-433 ◽  
Author(s):  
Michael Th. Rassias ◽  
Bicheng Yang
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Integral Inequality ◽  
Type Integral ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Hilbert Type

scholarly journals Two kinds of the reverse Hardy-type integral inequalities with the equivalent forms related to the extended Riemann zeta function

2018 ◽  
Vol 12 (2) ◽  
pp. 273-296 ◽  
Author(s):  
Michael Rassias ◽  
Bicheng Yang ◽  
Andrei Raigorodskii
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Integral Inequalities ◽  
Weight Functions ◽  
Real Analysis ◽  
Hardy Type ◽  
Type Integral ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Equivalent Conditions

Applying techniques of real analysis and weight functions, we study some equivalent conditions of two kinds of the reverse Hardy-type integral inequalities with a particular nonhomogeneous kernel. The constant factors are related to the Riemann zeta function and are proved to be best possible. In the form of applications, we deduce a few equivalent conditions of two kinds of the reverse Hardy-type integral inequalities with a particular homogeneous kernel. We also consider some corollaries as particular cases.

Universality of $L$-Dirichlet functions and nontrivial zeros of the Riemann zeta-function

2019 ◽  
Vol 210 (12) ◽  
pp. 1753-1773 ◽  
Author(s):  
A. Laurinčikas ◽  
J. Petuškinaitė
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Nontrivial Zeros ◽  
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 .

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