On algebraic differential properties of the Riemann ζ-function and the Euler Γ-function

DOI10.1080/17476930903394788zbMath1216.33007OpenAlexW2122153046MaRDI QIDQ3168683

Zhuan Ye, Bao Qin Li

Publication date: 19 April 2011

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930903394788

zbMATH Keywords

polynomialRiemann \(\zeta\)-functionalgebraic 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) Differential algebra (12H05) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (10)

Algebraic differential independence concerning the Euler \(\Gamma\)-function and Dirichlet series ⋮ On the differential and difference independence of \(\Gamma\) and \(\zeta\) ⋮ Algebraic differential equations with functional coefficients concerning \(\zeta\) and \(\Gamma\) ⋮ 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 \(\zeta\) ⋮ Unnamed Item ⋮ 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

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• A note on Hölder's theorem concerning the Gamma function
• The Nevanlinna functions of the Riemann zeta-function
• Differential independence of \(\Gamma\) and \(\zeta\)
• Difference independence of the Riemann zeta function
• On differential independence of the Riemann zeta function and the Euler gamma function
• On some new properties of the gamma function and the Riemann zeta function

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