Algebraic differential independence regarding the Riemann \(\boldsymbol{\zeta}\)-function and the Euler \(\boldsymbol{\Gamma}\)-function

DOI10.1016/j.jnt.2019.12.006zbMath1459.11167arXiv1811.04188OpenAlexW3002164529WikidataQ114157209 ScholiaQ114157209MaRDI QIDQ2220446

Jingbo Liu, Qi Han

Publication date: 25 January 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.04188

zbMATH Keywords

Riemann zeta functionalgebraic differential equationEuler gamma function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Differential algebra (12H05) Meromorphic functions of one complex variable (general theory) (30D30) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (2)

On the differential and difference independence of \(\Gamma\) and \(\zeta\) ⋮ On the algebraic differential independence of \(\Gamma\) and \(\zeta\)

Cites Work

• Does the Riemann zeta function satisfy a differential equation?
• Some uniqueness results related to \(L\)-functions
• Algebraic differential equations with functional coefficients concerning \(\zeta\) and \(\Gamma\)
• On the distribution of nonzero values of the Riemann \(\zeta\)-function
• A note on Hölder's theorem concerning the Gamma function
• The Nevanlinna functions of the Riemann zeta-function
• Differential independence of \(\Gamma\) and \(\zeta\)
• Algebraic differential equations concerning the Riemann zeta function and the Euler gamma function
• On the eigenvalues in problems with spherical symmetry
• On differential independence of the Riemann zeta function and the Euler gamma function
• A result on value distribution of L-functions

This page was built for publication: Algebraic differential independence regarding the Riemann \(\boldsymbol{\zeta}\)-function and the Euler \(\boldsymbol{\Gamma}\)-function