scholarly journals On the periodic zeta-function with rational parameter

2011 ◽  
Vol 52 ◽  
Author(s):  
Sondra Černigova
Keyword(s):  
Asymptotic Formula ◽  
Zeta Function ◽  
Error Term ◽  
Fourth Power ◽  
Power Moment ◽  
Rational Parameter ◽  
Estimated Error

We obtain an asymptotic formula with estimated error term for the fourth power moment of the periodic zeta-function with rational parameter.

scholarly journals On the fourth power moment of the error term for the divisor problem with congruence conditions

2018 ◽  
Vol 14 (06) ◽  
pp. 1525-1546 ◽  
Author(s):  
Jinjiang Li ◽  
Min Zhang
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Congruence Class ◽  
Divisor Problem ◽  
Fourth Power ◽  
Power Moment ◽  
Higher Power ◽  
Power Moments

Let [Formula: see text] denote the number of factorizations [Formula: see text], where each of the factors [Formula: see text] belongs to a prescribed congruence class [Formula: see text]. Let [Formula: see text] be the error term of the asymptotic formula of [Formula: see text]. In this paper, we establish an asymptotic formula of the fourth power moment of [Formula: see text] and prove that [Formula: see text] with [Formula: see text], which improves the previous value [Formula: see text] of Liu [On higher-power moments of the error term for the divisor problem with congruence conditions, Monatsh. Math. 163(2) (2011) 175–195].

On the Riemann–Siegel formula

2007 ◽  
Vol 463 (2086) ◽  
pp. 2557-2568 ◽  
Author(s):  
A Kuznetsov
Keyword(s):  
Asymptotic Formula ◽  
Zeta Function ◽  
Critical Point ◽  
Riemann Zeta Function ◽  
Error Term ◽  
Error Function ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

In this article, we derive a generalization of the Riemann–Siegel asymptotic formula for the Riemann zeta function. By subtracting the singularities closest to the critical point, we obtain a significant reduction of the error term at the expense of a few evaluations of the error function. We illustrate the efficiency of this method by comparing it to the classical Riemann–Siegel formula.

scholarly journals A note on the 2 k-th mean value of the Hurwitz zeta function

1999 ◽  
Vol 60 (3) ◽  
pp. 403-405 ◽  
Author(s):  
A. Kumchev
Keyword(s):  
Asymptotic Formula ◽  
Zeta Function ◽  
Error Term ◽  
Mean Value ◽  
Substantial Improvement ◽  
Hurwitz Zeta Function ◽  
Image Position

Consider the error term in the asymptotic formulaIn this note we obtain δ(k) ≍ 1/(k6 log2k) which, for large values of k, presents a substantial improvement over the previously known result .

On the seventh power moment of Δ(x)

2017 ◽  
Vol 13 (03) ◽  
pp. 571-591
Author(s):  
Jinjiang Li
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Divisor Problem ◽  
Power Moment ◽  
Dirichlet Divisor Problem

Let [Formula: see text] be the error term of the Dirichlet divisor problem. In this paper, we establish an asymptotic formula of the seventh-power moment of [Formula: see text] and prove that [Formula: see text] with [Formula: see text] which improves the previous result.

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