Web9 jan. 2024 · EDIT 1: The question is strictly about the continued fraction method. I know the result I have to reach, the polynomial represents an unstable system. I don't want … Web(On the other hand, to my knowledge no particular algebraic number has been proven to have unbounded coefficients in its Hurwitz $\mathbb{Z}[i]$-continued fractions expansion.) But now there is something even more curious about the implication of such examples for Roth's theorem over $\mathbb{Q}(i)$ (diophantine approximations by …
On Salem numbers, expansive polynomials and Stieltjes continued fractions
WebContinued fraction expansion, Diophantine approximation. 1. Hurwitz’s algorithm Let x be a complex number such that x–Q.i/. ˘e (positive) Hurwitz continued fraction expansion … WebMore specifically, we consider the set E ( ψ) of complex numbers which are well approximated with the given bound ψ and have quite different Hurwitz continued fraction expansions from that of their rational approximations. The Hausdorff and packing dimensions of such set are determined. all clear communication
Complex Continued Fraction Algorithms - Mathematics
Web24 mrt. 2024 · Hurwitz Number. A number with a continued fraction whose terms are the values of one or more polynomials evaluated on consecutive integers and then … Web4 jan. 2024 · The convergents of a continued fraction of an irrational number provide the \best" approximations by rationals. Also, we know that the continued fraction expansion of a real number is essentially unique Let [a 0;a 1;a 2;:::] denotes the continued fraction a 0 + 1 a 1 + 1 a 2 + It is well know that the continued fraction for ˘terminates if and ... WebIn the case of Complex Continued Fractions the origins can easily be traced back to the end of the 19th century (see [Perron, 1954, vl. 1, Ch. 46]). One of their godfathers had … allclear cordless mosquito mister