<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this article, we have studied the uniqueness problem of Dirichlet series, which is convergent in a right half-plane and having analytic continuation in the complex plane as a meromorphic function sharing some sets and values. Our first result partially improve a result of [Ann. Univ. Sci. Budapest., Sect. Comput., <bold>48</bold>(2018), 117-128] by relaxing the sharing conditions. Most importantly, we have pointed out a number of big gaps in a recent paper [J. Contemp. Math. Anal., <bold>56</bold>(2021), 80-86], which makes the existence of the paper under question. Finally, under a different approach, we have provided the corrected form of the result of [J. Contemp. Math. Anal., <bold>56</bold>(2021), 80-86] as much as practicable.</p>
</abstract>

In this article, we have studied the uniqueness problem of Dirichlet series, which is convergent in a right half-plane and having analytic continuation in the complex plane as a meromorphic function sharing some sets and values. Our first result partially improve a result of [Ann. Univ. Sci. Budapest., Sect. Comput., 48(2018), 117-128] by relaxing the sharing conditions. Most importantly, we have pointed out a number of big gaps in a recent paper [J. Contemp. Math. Anal., 56(2021), 80-86], which makes the existence of the paper under question. Finally, under a different approach, we have provided the corrected form of the result of [J. Contemp. Math. Anal., 56(2021), 80-86] as much as practicable.

Uniqueness of Dirichlet series in the light of shared set and values

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Uniqueness of Dirichlet series in the light of shared set and values"}

In this article, we have studied the uniqueness problem of Dirichlet series, which is convergent in a right half-plane and having analytic continuation in the...

Uniqueness of Dirichlet series in the light of shared set and values

Published Online: Dec 26, 2023

Page range: 230 - 243

Received: Sep 25, 2022

DOI: https://doi.org/10.2478/ausm-2023-0012

Keywords
Dirichlet series, convergence, uniqueness, shared sets

© 2023 Abhijit Banerjee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Uniqueness of Dirichlet series in the light of shared set and values

Published Online: Dec 26, 2023

Page range: 230 - 243

Received: Sep 25, 2022

DOI: https://doi.org/10.2478/ausm-2023-0012

KeywordsDirichlet series, convergence, uniqueness, shared sets

© 2023 Abhijit Banerjee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Dirichlet series, convergence, uniqueness, shared sets