Linear independence of \(q\)-analogues of certain classical constants

DOI10.1007/BF03323010zbMath1128.11035OpenAlexW2000599887MaRDI QIDQ1781903

Keijo Väänänen, Peter Bundschuh

Publication date: 9 June 2005

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03323010

zbMATH Keywords

Lambert serieslinear independence

Mathematics Subject Classification ID

Irrationality; linear independence over a field (11J72)

Related Items

Linear independence of certain Lambert series ⋮ Hermite-Padé rational approximation to irrational numbers ⋮ A \(q\)-analogue of the Bailey-Borwein-Bradley identity ⋮ Unnamed Item ⋮ IRRATIONALITY OF LAMBERT SERIES ASSOCIATED WITH A PERIODIC SEQUENCE ⋮ Linear and algebraic independence of functions associated to a \(q\)-zeta function ⋮ Remarks on linear independence of \(q\)-harmonic series ⋮ Linear independence of \(q\)-logarithms over the Eisenstein integers ⋮ Irrationality of \(\zeta _{q}(1)\) and \(\zeta _{q}(2)\) ⋮ On the irrationality of generalized \(q\)-logarithm

Cites Work

• Approximations to \(q\)-logarithms and \(q\)-dilogarithms, with applications to \(q\)-zeta values
• Linear independence of the values of transcendental solutions of certain functional equations.
• Irrationality of certain Lambert series
• On the irrationality of \(\sum (1/(q^ n+r))\)
• Modular functions and transcendence questions
• Heine's basic transform and a permutation group for q-harmonic series
• ARITHMETICAL RESULTS ON CERTAIN MULTIVARIATE POWER SERIES
• On the irrationality of certain series