Illinois Journal of Mathematics

On representations of error terms related to the derivatives for some Dirichlet series

Jun Furuya, T. Makoto Minamide, and Yoshio Tanigawa

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Abstract

In previous papers, we examined several properties of an error term in a certain divisor problem related to the derivatives of the Riemann zeta-function. In this paper, we obtain representations of error terms related to the derivatives of some Dirichlet series, which can be regarded as generalized versions of a Dirichlet divisor problem and a Gauss circle problem. We also give the upper bounds of the error terms in terms of exponent pairs.

Article information

Source
Illinois J. Math., Volume 61, Number 1-2 (2017), 187-209.

Dates
Received: 3 April 2017
Revised: 16 October 2017
First available in Project Euclid: 3 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1520046215

Digital Object Identifier
doi:10.1215/ijm/1520046215

Mathematical Reviews number (MathSciNet)
MR3770842

Zentralblatt MATH identifier
06864465

Subjects
Primary: 11N37: Asymptotic results on arithmetic functions

Citation

Furuya, Jun; Minamide, T. Makoto; Tanigawa, Yoshio. On representations of error terms related to the derivatives for some Dirichlet series. Illinois J. Math. 61 (2017), no. 1-2, 187--209. doi:10.1215/ijm/1520046215. https://projecteuclid.org/euclid.ijm/1520046215


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