Patterns of Continued Fractions for the Analogues ofeand Related Numbers in the Function Field Case
✍ Scribed by Dinesh S Thakur
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 371 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
Patterns for simple continued fractions of the analogues of (xe 2Âf +y)Â(ze 2Âf +w) in the F q [t] case are described. In contrast to the classical case where they consist of arithmetic progressions, in this case they involve an interesting inductive scheme of block repetition and reversals, especially for q=2.
1997 Academic Press
This is a sequel to [T2]. For perspective, motivation, and background material on continued fractions and the Carlitz exponential, the reader may profit from looking at [BS, T1, T2], but this paper is mostly self-contained. We start with a brief introduction: 0.0. Classical results of Euler and Hurwitz ([H1], [P]) show that the sequence of partial quotients for the (simple) continued fraction for (xe 2Âf +y)Â(ze 2Âf +w), with x, y, z, w, f integers, f {0, xw&yz{0 (the socalled Hurwitz numbers), eventually consist of a fixed number of arithmetic progressions.
Examples.