scholarly journals On the mean square value of the Hurwitz zeta-function

1994 ◽  
Vol 38 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Zhang Wenpeng
Keyword(s):  
Zeta Function ◽  
Hurwitz Zeta Function ◽  
Mean Square ◽  
The Mean

scholarly journals Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 754 ◽  
Author(s):  
A. C. L. Ashton ◽  
A. S. Fokas
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Formal Proof ◽  
Hurwitz Zeta Function ◽  
Mean Square ◽  
Novel Approach ◽  
Starting Point ◽  
Lindelöf Hypothesis ◽  
Riemann Zeta ◽  
The Mean

In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean square of the Hurwitz zeta function. Also, a relation derived here provides the starting point of a novel approach which, in a series of companion papers, yields a formal proof of the Lindelöf hypothesis. Some of the above relations motivate the need for analysing the large α behaviour of the modified Hurwitz zeta function ζ 1 ( s , α ) , s ∈ C , α ∈ ( 0 , ∞ ) , which is also presented here.

scholarly journals Structural elucidation of the mean square of the Hurwitz zeta-function

2006 ◽  
Vol 120 (1) ◽  
pp. 101-119
Author(s):  
Shigeru Kanemitsu ◽  
Yoshio Tanigawa ◽  
Masami Yoshimoto
Keyword(s):  
Zeta Function ◽  
Structural Elucidation ◽  
Hurwitz Zeta Function ◽  
Mean Square ◽  
The Mean

scholarly journals On the mean square of the Riemann zeta function and the divisor problem

2008 ◽  
Vol 83 (97) ◽  
pp. 71-86
Author(s):  
Yifan Yang
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Integral Transforms ◽  
Divisor Problem ◽  
Mean Square ◽  
The Riemann Zeta Function ◽  
Dirichlet Divisor Problem ◽  
Error Terms ◽  
Riemann Zeta ◽  
The Mean

Let ?(T) and E(T) be the error terms in the classical Dirichlet divisor problem and in the asymptotic formula for the mean square of the Riemann zeta function in the critical strip, respectively. We show that ?(T) and E(T) are asymptotic integral transforms of each other. We then use this integral representation of ?(T) to give a new proof of a result of M. Jutila.

scholarly journals THE MEAN SQUARE OF THE LOGARITHM OF THE ZETA-FUNCTION

2000 ◽  
Vol 42 (2) ◽  
pp. 157-166 ◽  
Author(s):  
MICHEL BALAZARD ◽  
ALEKSANDAR IVIĆ
Keyword(s):  
Zeta Function ◽  
Mean Square ◽  
The Mean
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