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A Certain Power Series and the Inhomogeneous Continued Fraction Expansions

โœ Scribed by Takao Komatsu

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
607 KB
Volume
59
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

A recent paper (J. Number Theory 42 (1992), 61 87) announced various arithmetical properties of the Mahler function f (%, ,; x, y)= k=1 1 m k%+, x k y m . Unfortunately the arguments of that paper are marred by an error whereby the arguments hold only for ,=0 (or when b n =1 for all positive integers n). We show how to correct the arguments so that they do hold for general ,. Moreover, another paper (J. Number Theory 43 (1993), 293 318) soon afterwards happened again to discuss the subject using different expressions for the power series for f. We show that the corrected results here do coincide with those later results notwithstanding our alternative presentation.

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โœ M.W. Buck; D.P. Robbins ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 280 KB

Some time ago Mills and Robbins (1986, J. Number Theory 23, No. 3, 388-404) conjectured a simple closed form for the continued fraction expansion of the power series solution \(f=a_{1} x^{-1}+a_{2} x^{-2}+\cdots\) to the equation \(f^{4}+f^{2}-x f+1=0\) when the base field is GF(3). In this paper we