Approximations to \(q\)-logarithms and \(q\)-dilogarithms, with applications to \(q\)-zeta values

DOI10.1007/s10958-006-0263-yzbMath1088.11052OpenAlexW1990290043MaRDI QIDQ558747

Wadim Zudilin

Publication date: 14 July 2005

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/231004

zbMATH Keywords

Diophantine approximations\(q\)-dilogarithms\(q\)-logarithms\(q\)-zeta values

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Other Dirichlet series and zeta functions (11M41) Measures of irrationality and of transcendence (11J82)

Related Items

Linear independence of certain Lambert series ⋮ Hermite-Padé rational approximation to irrational numbers ⋮ On the summability of bivariate rational functions ⋮ A \(q\)-analogue of the Bailey-Borwein-Bradley identity ⋮ Linear independence of \(q\)-logarithms over the Eisenstein integers ⋮ Sums of series of Rogers dilogarithm functions ⋮ Linear independence of \(q\)-analogues of certain classical constants ⋮ Irrationality of \(\zeta _{q}(1)\) and \(\zeta _{q}(2)\) ⋮ On the irrationality of generalized \(q\)-logarithm ⋮ Leonhard Euler and a 𝑞-analogue of the logarithm

Cites Work

• Linear independence of the values of transcendental solutions of certain functional equations.
• Little \(q\)-Legendre polynomials and irrationality of certain Lambert series.
• Diophantine problems for \(q\)-zeta values
• On the irrationality of \(\sum (1/(q^ n+r))\)
• On the irrationality measure for a $ q$-analogue of $ \zeta(2)$
• Rational approximations to π and some other numbers
• Heine's basic transform and a permutation group for q-harmonic series
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