We consider the continued fraction expansion of certain algebraic formal power series when the base field is finite. We are concerned with the property of the sequence of partial quotients being bounded or unbounded. We formalize the approach introduced by Baum and Sweet (1976), which applies to the
Algebraic and Badly Approximable Power Series over a Finite Field
โ Scribed by Alain Lasjaunias; Jean-Jacques Ruch
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 324 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1071-5797
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โฆ Synopsis
We will exhibit certain continued fraction expansions for power series over a "nite "eld, with all the partial quotients of degree one, which are non-quadratic algebraic elements over the "eld of rational functions.
๐ SIMILAR VOLUMES
We define and describe a class of algebraic continued fractions for power series over a finite field. These continued fraction expansions, for which all the partial quotients are polynomials of degree one, have a regular pattern induced by the Frobenius homomorphism.This is an extension, in the case
If p is an odd prime, then denote by % N the "eld with p elements. We prove that a certain "vefold is modular in the sense that for every odd p, the number of its points over % N is predicted explicitly by the pth coe$cient of the Fourier expansion of the weight 6 modular form (2z).