On the generating function of the integer part: \([n\alpha{}+ \gamma{}]\)

DOI10.1006/jnth.1993.1023zbMath0778.11039OpenAlexW2040087553WikidataQ56935932 ScholiaQ56935932MaRDI QIDQ1803890

Jonathan M. Borwein, Peter B. Borwein

Publication date: 29 June 1993

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1993.1023

zbMATH Keywords

continued fraction expansionsfunctional equationspecial functionsidentitytranscendental numbersgreatest integer functionnon-homogeneous diophantine approximation problempartition of the set of positive integers

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Continued fractions and generalizations (11J70) Arithmetic progressions (11B25) Inhomogeneous linear forms (11J20)

Related Items (14)

On sums of fractional parts \(\{na+y\}\) ⋮ The fractional part of \(n\theta + \phi\) and Beatty sequences ⋮ Nonnormality of Stoneham constants ⋮ Results on fractional parts of linear functions of n and applications to Beatty sequences ⋮ On the one-sided boundedness of sums of fractional parts \((\{ n\alpha+ \gamma\}-\frac12)\). ⋮ Symmetry and specializability in the continued fraction expansions of some infinite products ⋮ A generating function technique for Beatty sequences and other step sequences ⋮ Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series ⋮ Lifshitz tails at spectral edge and holography with a finite cutoff ⋮ Algebraic independence of the values of certain series and their derivatives involving the Hecke-Mahler series ⋮ Substitution invariant Sturmian bisequences ⋮ Random Generators and Normal Numbers ⋮ Algebraic independence of certain numbers ⋮ Applications of standard Sturmian words to elementary number theory

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