ON THE MEAN SQUARE OF THE RIEMANN ZETA-FUNCTION

1987 ◽  
Vol 38 (3) ◽  
pp. 337-343 ◽  
Author(s):  
TOM MEURMAN
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Mean Square ◽  
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.

Omega result for the mean square of the Riemann zeta function

2005 ◽  
Vol 117 (3) ◽  
pp. 373-381 ◽  
Author(s):  
Yuk-Kam Lau ◽  
Kai-Man Tsang
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Mean Square ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
The Mean

scholarly journals On the mean square of the Riemann zeta-function in short intervals

2009 ◽  
Vol 85 (99) ◽  
pp. 1-17 ◽  
Author(s):  
Aleksandar Ivic
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Mean Square ◽  
Short Intervals ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
The Mean

It is proved that, for T? ? G = G(T)? ??T, ?T2T(I1(t+G,G)- I1(t,G))2 dt = TG ?aj logj (?T/G)+ O?(T1+? G1/2+ +T1/2?G? with some explicitly computable constants aj(a3>0)where, for fixed K ? N, Ik(t,G)= 1/?? ? ? -? |?(1/2 + it + iu)|2k e -(u/G)?du. The generalizations to the mean square of I1(t+U,G)-I1(t,G) over [T,T+H] and the estimation of the mean square of I2(t+ U,G) - I2(t,G) are also discussed.

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