scholarly journals Limit theorems for the Mellin transform of the square of the Riemann zeta-function. I

2006 ◽  
Vol 122 (2) ◽  
pp. 173-184 ◽  
Author(s):  
Antanas Laurinčikas
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Limit Theorems ◽  
Mellin Transform ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

scholarly journals A two-dimensional limit discrete theorem for Mellin transforms of the Riemann zeta-function

2007 ◽  
Vol 47 ◽  
Author(s):  
Violeta Balinskaitė
Keyword(s):  
Limit Theorem ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Mellin Transform ◽  
Two Dimensional ◽  
Mellin Transforms ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

In the paper two-dimensional limit theorem for the modified Mellin transform of the Riemann zeta-function is obtained.

scholarly journals A generalized Davenport expansion

2021 ◽  
pp. 1-5
Author(s):  
Alexander E. Patkowski
Keyword(s):  
Zeta Function ◽  
Infinite Series ◽  
Riemann Zeta Function ◽  
Fourier Expansion ◽  
Mellin Transform ◽  
Fractional Part ◽  
Arithmetic Functions ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Abstract We prove a new generalization of Davenport's Fourier expansion of the infinite series involving the fractional part function over arithmetic functions. A new Mellin transform related to the Riemann zeta function is also established.

ZERO-FREE REGIONS OF A q-ANALOGUE OF THE COMPLETE RIEMANN ZETA FUNCTION

2011 ◽  
Vol 07 (04) ◽  
pp. 1075-1092
Author(s):  
MITSUGU MERA
Keyword(s):  
Zeta Function ◽  
Theta Function ◽  
Riemann Zeta Function ◽  
Mellin Transform ◽  
Critical Strip ◽  
Jacobi Theta Function ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

A q-analogue of the complete Riemann zeta function presented in this paper is defined by the q-Mellin transform of the Jacobi theta function. We study zero-free regions of the q-zeta function. As a by-product, we show that the Riemann zeta function does not vanish in a sub-region of the critical strip.

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