Transcendence of power series for some number theoretic functions

DOI10.1090/S0002-9939-08-09737-2zbMath1236.11063arXiv0806.1563MaRDI QIDQ3623341

Michael Coons, Peter B. Borwein

Publication date: 17 April 2009

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

Full work available at URL: https://arxiv.org/abs/0806.1563

Mathematics Subject Classification ID

Power series (including lacunary series) in one complex variable (30B10) Transcendence (general theory) (11J81) Diophantine approximation, transcendental number theory (11J99) Real rational functions (26C15)

Related Items (10)

On the behavior of a power series with completely multiplicative coefficients near the unit circle ⋮ Power series approximations to Fekete polynomials ⋮ Rationality of Hilbert series in noncommutative invariant theory ⋮ (Non)Automaticity of number theoretic functions ⋮ Transcendence of some power series for Liouville number arguments ⋮ Mock characters and the Kronecker symbol ⋮ Multiplicative automatic sequences ⋮ Composition inverses of the variations of the Baum-Sweet sequence ⋮ Transcendence of generating functions whose coefficients are multiplicative ⋮ TRANSCENDENCE OVER MEROMORPHIC FUNCTIONS

Cites Work

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• Transcendence of formal power series with rational coefficients
• Multiplicative functions and \(k\)-automatic sequences
• Irrationality of power series for various number theoretic functions
• On the irrationality of \(\sum (1/(q^ n+r))\)
• Polynomials with coefficients from a finite set
• Modular functions and transcendence questions
• On the base-dependence of sets of numbers recognizable by finite automata
• Uniform tag sequences
• Power Series with Bounded Coefficients

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