Document Type
Article
Publication Date
1-13-2026
Abstract
We study the singularities of the Dirichlet series D ( s ) = ∑ n ≥ 1 h n n s
when the power series H ( z ) = ∑ n ≥ 0 h n z n
has a singularity of general type at the point z 0 = 1
. This extends a recent result of L.M. Navas, J. Ruiz, and J.L. Varona, and connects to foundational ideas explored by Hardy, Fekete, and others. The tools employed include classical methods from the theory of Dirichlet series, particularly those often used in connection with the Riemann zeta function, namely the Mellin transform and splitting methods. These techniques were also used by Navas, Ruiz, and Varona. The polylogarithm function plays a fundamental role in this work.
Recommended Citation
Sebbar, A., Gay, R., Dirichlet's series associated with some power series. J. Math. Anal. Appl. 558 (2026), 130408. https://doi.org/10.1016/j.jmaa.2026.130408
Peer Reviewed
1
Copyright
Elsevier
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Comments
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, volume 558, issue 2, in 2026. https://doi.org/10.1016/j.jmaa.2026.130408
The Creative Commons license below applies only to this version of the article.