Continued fraction expansion of algebraic numbers
โ Scribed by A.D. Bryuno
- Publisher
- Elsevier Science
- Year
- 1964
- Weight
- 816 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0041-5553
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
Given any solution triple of natural numbers to the Markoff equation a 2 +b 2 + c 2 =3abc, an old problem asks whether the largest number determines the triple uniquely. We show this to be true in a range of cases by considering the factorisation of ideals in certain quadratic number fields, but als
## It is proved that the function Yรฐzร which can be expressed as a certain continued fraction, takes algebraically independent values at any distinct nonzero algebraic numbers inside the unit circle if the sequence fR k g kX0 is the generalized Fibonacci numbers.