scholarly journals Ω±-results of the error term in the mean square formula of the Riemann zeta-function in the critical strip

2001 ◽  
Vol 98 (1) ◽  
pp. 53-69
Author(s):  
Yuk-Kam Lau ◽  
Kai-Man Tsang
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Error Term ◽  
Mean Square ◽  
Critical Strip ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
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.

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