Diophantine properties for 𝑞-analogues of Dirichlet’s beta function at positive integers

DOI10.1090/S0002-9947-2010-05236-5zbMath1217.11069arXiv0811.4287MaRDI QIDQ3085136

Elie Mosaki, Frédéric Jouhet

Publication date: 28 March 2011

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

Full work available at URL: https://arxiv.org/abs/0811.4287

zbMATH Keywords

modular formsirrationalitybasic hypergeometric series\(q\)-analogue of values of Dirichlet's beta function

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Other Dirichlet series and zeta functions (11M41) Irrationality; linear independence over a field (11J72)

Cites Work

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• Euler numbers, Padé approximants and Catalan's constant
• Diophantine properties of numbers related to Catalan's constant
• Little \(q\)-Legendre polynomials and irrationality of certain Lambert series.
• SÉRIES HYPERGÉOMÉTRIQUES BASIQUES, $q$-ANALOGUES DES VALEURS DE LA FONCTION ZÊTA ET SÉRIES D’EISENSTEIN
• On a linear form for Catalan's constant
• Irrationality measures for certain $q$-mathematical constants
• Modular functions and transcendence questions
• IRRATIONALITÉ AUX ENTIERS IMPAIRS POSITIFS D'UN q-ANALOGUE DE LA FONCTION ZÊTA DE RIEMANN

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