On the mean square of the error term for the asymmetric two-dimensional divisor problem (I)

2008 ◽  
Vol 159 (1-2) ◽  
pp. 185-209 ◽  
Author(s):  
Wenguang Zhai ◽  
Xiaodong Cao
Keyword(s):  
Error Term ◽  
Divisor Problem ◽  
Mean Square ◽  
Two Dimensional ◽  
The Mean

On the mean square of the error term for the asymmetric two-dimensional divisor problems(II)

2009 ◽  
Vol 160 (2) ◽  
pp. 115-142 ◽  
Author(s):  
Xxiaodong Cao ◽  
Wenguang Zhai
Keyword(s):  
Error Term ◽  
Mean Square ◽  
Two Dimensional ◽  
Divisor Problems ◽  
The Mean

The Mean Square of the Error Term in a Genelarization of the Dirichlet Divisor Problem

1997 ◽  
pp. 209-226 ◽  
Author(s):  
Kai-Yam Lam ◽  
Kai-Yam Tsang
Keyword(s):  
Error Term ◽  
Divisor Problem ◽  
Mean Square ◽  
Dirichlet Divisor Problem ◽  
The Mean

scholarly journals On some mean value results for the zeta-function and a divisor problem

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2315-2327
Author(s):  
Aleksandar Ivic
Keyword(s):  
Zeta Function ◽  
Error Term ◽  
Mean Value ◽  
Divisor Problem ◽  
Mean Square ◽  
Asymptotic Formulae ◽  
Dirichlet Divisor Problem ◽  
The Mean

Let ?(x) denote the error term in the classical Dirichlet divisor problem, and let the modified error term in the divisor problem be ?*(x) = -?(x) + 2?(2x)-1/2?(4x). We show that ?T+H,T ?*(t/2?)|?(1/2+it)|2dt<< HT1/6log7/2 T (T2/3+? ? H = H(T) ? T), ?T,0 ?(t)|?(1/2+it)|2dt << T9/8(log T)5/2, and obtain asymptotic formulae for ?T,0 (?*(t/2?))2|?( 1/2+it)|2 dt, ?T0 (?*(t/2?))3|?(1/+it)|2 dt. The importance of the ?*-function comes from the fact that it is the analogue of E(T), the error term in the mean square formula for |?(1/2+it)|2. We also show, if E*(T) = E(T)-2??*(T/(2?)), ?T0 E*(t)Ej(t)|?(1/2+it)|2 dt << j,? T7/6+j/4+? (j=1,2,3).

scholarly journals The mean square of the error term in a generalization of Dirichlet's divisor problem

1996 ◽  
Vol 74 (4) ◽  
pp. 351-364 ◽  
Author(s):  
Tom Meurman
Keyword(s):  
Error Term ◽  
Divisor Problem ◽  
Mean Square ◽  
The Mean

scholarly journals On the mean square formula of the error term in the Dirichlet divisor problem

2009 ◽  
Vol 146 (2) ◽  
pp. 277-287 ◽  
Author(s):  
YUK-KAM LAU ◽  
KAI-MAN TSANG
Keyword(s):  
Remainder Term ◽  
Error Term ◽  
Divisor Problem ◽  
Mean Square ◽  
The Riemann Zeta Function ◽  
Dirichlet Divisor Problem ◽  
Error Terms ◽  
Riemann Zeta ◽  
The Mean ◽  
Upper Estimate

AbstractLet F(x) be the remainder term in the mean square formula of the error term Δ(t) in the Dirichlet divisor problem. We improve on the upper estimate of F(x) obtained by Preissmann around twenty years ago. The method is robust, which applies to the same problem for the error terms in the circle problem and the mean square formula of the Riemann zeta-function.

scholarly journals The asymptotic behaviour of the mean-square of fractional part sums

2000 ◽  
Vol 43 (2) ◽  
pp. 309-323 ◽  
Author(s):  
Manfred Kühleitner ◽  
Werner Georg Nowak
Keyword(s):  
Asymptotic Formula ◽  
Asymptotic Behaviour ◽  
Error Term ◽  
Fractional Part ◽  
Mean Square ◽  
The Mean

AbstractIn this article we consider sums S(t) = Σnψ (tf(n/t)), where ψ denotes, essentially, the fractional part minus ½ f is a C4-function with f″ non-vanishing, and summation is extended over an interval of order t. For the mean-square of S(t), an asymptotic formula is established. If f is algebraic this can be sharpened by the indication of an error term.

The Mean Square of the Error Term for the Fourth Power Moment of the Zeta-Function

1994 ◽  
Vol s3-69 (2) ◽  
pp. 309-329 ◽  
Author(s):  
Aleksandar Ivić ◽  
Yoichi Motohashi
Keyword(s):  
Zeta Function ◽  
Error Term ◽  
Fourth Power ◽  
Mean Square ◽  
Power Moment ◽  
The Mean

scholarly journals Mean square of the error term in the asymmetric multidimensional divisor problem

2016 ◽  
Vol 54 (2) ◽  
pp. 173-193 ◽  
Author(s):  
Xiaodon Cao ◽  
Yoshio Tanigawa ◽  
Wenguang Zhai
Keyword(s):  
Error Term ◽  
Divisor Problem ◽  
Mean Square

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.

Sign in / Sign up

Export Citation Format

Share Document