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Algebraic differential independence concerning the Euler Γ-function and Dirichlet series

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Abstract

This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class \({\mathbb F}\) which contains Dirichlet ℒ-functions, ℒ-functions in the extended Selberg class, or some periodic functions. We prove that the Euler Γ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions ϕ with ρ(ϕ) < 1.

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Authors and Affiliations

  1. School of Sciences, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Wei Chen & Qiong Wang

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  1. Wei Chen
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  2. Qiong Wang
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Correspondence to Qiong Wang.

Additional information

This work of both authors was partially supported by Basic and Advanced Research Project of CQ CSTC (cstc2019jcyj-msxmX0107), and Fundamental Research Funds of Chongqing University of Posts and Telecommunications (CQUPT: A2018-125).

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Chen, W., Wang, Q. Algebraic differential independence concerning the Euler Γ-function and Dirichlet series. Acta Math Sci 40, 1035–1044 (2020). https://doi.org/10.1007/s10473-020-0411-3

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  • DOI: https://doi.org/10.1007/s10473-020-0411-3

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