Displaying similar documents to “Diophantine approximation in short intervals”

On inhomogeneous diophantine approximation with some quasi-periodic expressions, II

Takao Komatsu (1999)

Journal de théorie des nombres de Bordeaux

Similarity:

We consider the values concerning ℳ ( θ , φ ) = lim inf | q | → ∞ | q | | | q θ - φ | | where the continued fraction expansion of θ has a quasi-periodic form. In particular, we treat the cases so that each quasi-periodic form includes no constant. Furthermore, we give some general conditions satisfying ℳ ( θ , φ ) = 0 .

Polynomials of Pellian Type and Continued Fractions

Mollin, R. (2001)

Serdica Mathematical Journal

Similarity:

We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued...