Patterns of continued fractions for the analogues of \(e\) and related numbers in the function field case
type: Item
instance of: scholarly article
title: Patterns of continued fractions for the analogues of \(e\) and related numbers in the function field case
zbMATH Open document ID: 0888.11007
author: Dinesh S. Thakur
published in: Journal of Number Theory
publication date: 1997-09-22T00:00:00Z
review text: The author variously details and proves, and provides supporting evidence for computational results on the continued fraction expansion of appropriate values of the Carlitz-Drinfeld exponential \(e(z)\) in the case of characteristic \(q=2\), adding to his earlier results [\textit{D. Thakur}, J. Number Theory 41, 150-155 (1992; Zbl 0754.11019) and ibid. 59, 248-261 (1966; Zbl 0866.11004)]. There is here a very interesting analogy with the numerical case, where, it seems, there are highly structured Hurwitz continued fraction expansions essentially only for \(\exp(a/b)\) if \(a\) is \(1\), or \(2\); for that and related musings see, for a recent example, the reviewer's note [\textit{A. J. van der Poorten}, Nieuw Arch. Wiskd. 14, 221-230 (1996; Zbl 0862.11044)]. The case \(q=2\), explored here, is rather more complicated than the cases dealt with completely by the author in the previous papers cited. Presumably, it is in some sense a degenerate case of that work; a description in those terms might provide further insight. The present, rather interesting and readable paper is not yet complete and -- as the author invites his readers -- well deserves further study, simplification and extension.
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 11R58
zbMATH DE Number: 1061244
zbMATH Keywords: function field
zbMATH Keywords: computational results
zbMATH Keywords: continued fraction expansion
zbMATH Keywords: values of the Carlitz-Drinfeld exponential
zbMATH Keywords: characteristic 2
MaRDI profile type: Publication
full work available at URL: jnth.1997.2134
OpenAlex ID: W2127024419
cites work: Continued fractions of algebraic power series in characteristic 2
cites work: Q3134952
cites work: Q5581784
cites work: Q5801433
cites work: On continued fractions and finite automata
cites work: Continued fraction for the exponential for \(\mathbb{F}_ q[T]\)
cites work: Exponential and continued fractions
cites work: Q4714717
DOI: 10.1006/JNTH.1997.2134
description: scientific article; zbMATH DE number 1061244