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 Two-Dimentional Discrete Limit Theorem in the Space of Analytic Functions for Mellin Transforms of the Riemann Zeta-Function

2008 ◽  
Vol 13 (2) ◽  
pp. 159-167 ◽  
Author(s):  
V. Balinskaitė ◽  
V. Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Critical Line ◽  
Space Of Analytic Functions ◽  
Mellin Transforms ◽  
Convergence Of Probability Measures ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

In the paper, a two-dimentional discrete limit theorem in the sense of weak convergence of probability measures in the space of analytic functions for Mellin transforms of the Riemann zeta-function on the critical line is obtained.

scholarly journals Some Mellin transforms for the Riemann zeta function in the critical strip

2019 ◽  
Vol 15 (01) ◽  
pp. 153-156
Author(s):  
Alexander E Patkowski
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Mellin Transform ◽  
Critical Strip ◽  
Mellin Transforms ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Fourier Integrals ◽  
The Way

We offer two new Mellin transform evaluations for the Riemann zeta function in the region [Formula: see text]. Some discussion is offered in the way of evaluating some further Fourier integrals involving the Riemann xi function.

scholarly journals Local limit theorem for coefficients of modified Borwein’s algorithm, proved by the ratio method

2019 ◽  
Vol 60 ◽  
pp. 11-14
Author(s):  
Igoris Belovas
Keyword(s):  
Limit Theorem ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Ratio Method ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

The paper continues the research of the modified Borwein method for the evaluation of the Riemann zeta-function. It provides a different perspective on the derivation of the local limit theorem for coefficients of the method. The approach is based on the ratio method, proposed by Proschan.  

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