Representations and evaluations of the error term in a certain divisor problem

AbstractIn this paper, we shall derive representations of the Chowla-Walum type formula for the error term in a divisor problem related to the derivatives of the Riemann zeta-function. As a direct corollary of this formula, we shall consider estimations of this error term.

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Counting distinct zeros of the Riemann zeta-function

The Electronic Journal of Combinatorics ◽

10.37236/1195 ◽

1994 ◽

Vol 2 (1) ◽

Author(s):

David W. Farmer

Keyword(s):

Zeta Function ◽

Riemann Zeta Function ◽

Simple Zeros ◽

The Riemann Zeta Function ◽

Riemann Zeta ◽

Derivatives Of

Bounds on the number of simple zeros of the derivatives of a function are used to give bounds on the number of distinct zeros of the function.

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Evaluating Fractional Derivatives of the Riemann Zeta Function

Lecture Notes in Computer Science - Mathematical Software – ICMS 2020 ◽

10.1007/978-3-030-52200-1_9 ◽

2020 ◽

pp. 94-101

Author(s):

Ricky E. Farr ◽

Sebastian Pauli ◽

Filip Saidak

Keyword(s):

Zeta Function ◽

Riemann Zeta Function ◽

Fractional Derivatives ◽

The Riemann Zeta Function ◽

Riemann Zeta ◽

Derivatives Of

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Some $\Omega$-results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem

Journal de Théorie des Nombres de Bordeaux ◽

10.5802/jtnb.188 ◽

1997 ◽

Vol 9 (1) ◽

pp. 41-50

Author(s):

Jerzy Kaczorowski ◽

Bogdan Szydło

Keyword(s):

Zeta Function ◽

Riemann Zeta Function ◽

Divisor Problem ◽

Fourth Power ◽

Power Moment ◽

The Riemann Zeta Function ◽

Additive Divisor Problem ◽

Riemann Zeta ◽

Additive Divisor

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Lower bounds of discrete moments of the derivatives of the Riemann zeta-function on the critical line

Journal de Théorie des Nombres de Bordeaux ◽

10.5802/jtnb.836 ◽

2013 ◽

Vol 25 (2) ◽

pp. 285-305 ◽

Cited By ~ 1

Author(s):

Thomas Christ ◽

Justas Kalpokas

Keyword(s):

Zeta Function ◽

Lower Bounds ◽

Riemann Zeta Function ◽

Critical Line ◽

The Riemann Zeta Function ◽

Riemann Zeta ◽

Discrete Moments ◽

Derivatives Of

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Computation of the derivatives of the riemann zeta-function in the complex domain

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(88)90121-8 ◽

1988 ◽

Vol 28 (4) ◽

pp. 115-124

Author(s):

A.Yu. Yeremin ◽

I.E. Kaporin ◽

M.K. Kerimov

Keyword(s):

Zeta Function ◽

Riemann Zeta Function ◽

Complex Domain ◽

The Riemann Zeta Function ◽

Riemann Zeta ◽

Derivatives Of

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On the riemann zeta-function and the divisor problem

Central European Journal of Mathematics ◽

10.2478/bf02475958 ◽

2004 ◽

Vol 2 (4) ◽

pp. 494-508 ◽

Cited By ~ 6

Author(s):

Aleksandar Ivić

Keyword(s):

Zeta Function ◽

Riemann Zeta Function ◽

Divisor Problem ◽

The Riemann Zeta Function ◽

Riemann Zeta

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

Journal of the London Mathematical Society ◽

10.1112/s0024610799007590 ◽

1999 ◽

Vol 60 (1) ◽

pp. 21-32 ◽

Cited By ~ 2

Author(s):

Aleksandar Ivić

Keyword(s):

Zeta Function ◽

Riemann Zeta Function ◽

Error Term ◽

Fourth Moment ◽

The Riemann Zeta Function ◽

Riemann Zeta

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On the zeros of linear combinations of derivatives of the Riemann zeta function, II

International Journal of Number Theory ◽

10.1142/s1793042118500252 ◽

2018 ◽

Vol 14 (02) ◽

pp. 371-382

Author(s):

K. Paolina Koutsaki ◽

Albert Tamazyan ◽

Alexandru Zaharescu

Keyword(s):

Asymptotic Formula ◽

Zeta Function ◽

Dirichlet Series ◽

Riemann Zeta Function ◽

Linear Combinations ◽

The Real ◽

The Riemann Zeta Function ◽

Unique Integer ◽

Riemann Zeta ◽

Derivatives Of

The relevant number to the Dirichlet series [Formula: see text], is defined to be the unique integer [Formula: see text] with [Formula: see text], which maximizes the quantity [Formula: see text]. In this paper, we classify the set of all relevant numbers to the Dirichlet [Formula: see text]-functions. The zeros of linear combinations of [Formula: see text] and its derivatives are also studied. We give an asymptotic formula for the supremum of the real parts of zeros of such combinations. We also compute the degree of the largest derivative needed for such a combination to vanish at a certain point.

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