On the Error Term for the Fourth Moment of the Riemann Zeta-Function

1999 ◽  
Vol 60 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Aleksandar Ivić
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Error Term ◽  
Fourth Moment ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

scholarly journals Ingham Tauberian theorem with an estimate for the error term

2003 ◽  
Vol 2003 (64) ◽  
pp. 4025-4031
Author(s):  
E. P. Balanzario ◽  
E. Marmolejo-Olea
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Tauberian Theorem ◽  
Error Term ◽  
Elementary Proof ◽  
Weak Form ◽  
Free Region ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

We estimate the error term in the Ingham Tauberian theorem. This estimation of the error term is accomplished by considering an elementary proof of a weak form of Wiener's general Tauberian theorem and by using a zero-free region for the Riemann zeta function.

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.

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