Patterns of continued fractions for the analogues of \(e\) and related numbers in the function field case
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.
values of the Carlitz-Drinfeld exponential
scientific article; zbMATH DE number 1061244