Algebraic differential equations with functional coefficients concerning \(\zeta\) and \(\Gamma\)

DOI10.1016/j.jde.2015.09.035zbMath1353.34110OpenAlexW2188896007MaRDI QIDQ890200

Bao Qin Li, Zhuan Ye

Publication date: 9 November 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.09.035

zbMATH Keywords

Riemann zeta functionpolynomialalgebraic differential equationEuler gamma function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (13)

Algebraic differential independence concerning the Euler \(\Gamma\)-function and Dirichlet series ⋮ On the differential and difference independence of \(\Gamma\) and \(\zeta\) ⋮ On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function ⋮ Difference independence of the Euler gamma function ⋮ On the difference independence of the Euler gamma function and the Riemann zeta function ⋮ On the algebraic difference independence of the Euler gamma function \(\Gamma\) and Dirichlet series ⋮ On the algebraic differential independence of \(\Gamma\) and \(\zeta\) ⋮ Hypertranscendency of perturbations of hypertranscendental functions ⋮ Unnamed Item ⋮ Algebraic differential independence regarding the Riemann \(\boldsymbol{\zeta}\)-function and the Euler \(\boldsymbol{\Gamma}\)-function ⋮ A study on algebraic differential equations of gamma function and Dirichlet series ⋮ ON ALGEBRAIC DIFFERENTIAL EQUATIONS FOR THE GAMMA FUNCTION AND -FUNCTIONS IN THE EXTENDED SELBERG CLASS ⋮ On algebraic differential equations of gamma function and Riemann zeta function

Cites Work

• Unnamed Item
• Value distribution of \(L\)-functions
• A note on Hölder's theorem concerning the Gamma function
• Differential independence of \(\Gamma\) and \(\zeta\)
• Algebraic differential equations concerning the Riemann zeta function and the Euler gamma function
• On algebraic differential properties of the Riemann ζ-function and the Euler Γ-function
• Difference independence of the Riemann zeta function
• On differential independence of the Riemann zeta function and the Euler gamma function
• Functional independence of the singularities of a class of Dirichlet series
• О функциональной независимости L-функций Дирихле
• On some new properties of the gamma function and the Riemann zeta function

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