Algebraic differential independence concerning the Euler Γ-function and Dirichlet series
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DOI: 10.1007/s10473-020-0411-3
Abstract: This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class $${\mathbb F}$$ F which contains Dirichlet ℒ -functions, ℒ -functions in the extended Selberg class, or… read more here.
Keywords: independence concerning; euler function; algebraic differential; differential independence ... See more keywords
ON ALGEBRAIC DIFFERENTIAL EQUATIONS FOR THE GAMMA FUNCTION AND -FUNCTIONS IN THE EXTENDED SELBERG CLASS
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DOI: 10.1017/s000497271700020x
Abstract: This paper concerns the problem of algebraic differential independence of the gamma function and ${\mathcal{L}}$ -functions in the extended Selberg class. We prove that the two kinds of functions cannot satisfy a class of algebraic… read more here.
Keywords: class; extended selberg; algebraic differential; gamma function ... See more keywords
Painlevé Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations
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DOI: 10.1155/2019/9210725
Abstract: In this paper, a class of nonlinear algebraic differential equations (NADEs) is studied. The Painlevé analysis of the NADEs is considered. Abundant meromorphic solutions of the NADEs are obtained by means of the complex method.… read more here.
Keywords: abundant meromorphic; nonlinear algebraic; algebraic differential; class nonlinear ... See more keywords
On algebraic differential equations of gamma function and Riemann zeta function
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DOI: 10.5186/aasfm.2019.4455
Abstract: Abstract. Due to Voronin’s universality theorem and Riemann–von Mangoldt formula, this paper concerns the problem of algebraic differential independence between the gamma function Γ and the function f(ζ), where ζ is the Riemann zeta function… read more here.
Keywords: gamma function; algebraic differential; riemann; riemann zeta ... See more keywords