Linear independence of certain Lambert series

DOI10.1090/S0002-9939-2014-12102-2zbMath1305.11063OpenAlexW1999284923MaRDI QIDQ3190323

Florian Luca, Yohei Tachiya

Publication date: 16 September 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2014-12102-2

zbMATH Keywords

Lambert serieslinear independencearithmetic functions

Mathematics Subject Classification ID

Irrationality; linear independence over a field (11J72)

Related Items (4)

GENERALIZED LAMBERT SERIES, RAABE’S COSINE TRANSFORM AND A GENERALIZATION OF RAMANUJAN’S FORMULA FOR ⋮ Linear independence of certain numbers ⋮ Refinement of the Chowla-Erdős method and linear independence of certain Lambert series ⋮ Generalized Lambert series and arithmetic nature of odd zeta values

Cites Work

• Approximations to \(q\)-logarithms and \(q\)-dilogarithms, with applications to \(q\)-zeta values
• There are infinitely many Carmichael numbers
• Linear independence of \(q\)-analogues of certain classical constants
• Irrationality of certain Lambert series
• Approximate formulas for some functions of prime numbers
• On the irrationality of \(\sum (1/(q^ n+r))\)
• Heine's basic transform and a permutation group for q-harmonic series
• Arithmetical functions and irrationality of Lambert series
• On the irrationality of certain series
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