scholarly journals On the error term of the mean square formula for the Riemann zeta-function in the critical strip 3/4<σ<1

2002 ◽  
Vol 102 (2) ◽  
pp. 157-165
Author(s):  
Yuk-Kam Lau
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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