Transcendence with Rosen Continued Fractions

نویسندگان

  • YANN BUGEAUD
  • THOMAS A. SCHMIDT
چکیده

We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Maillet–baker Continued Fractions

We use the Schmidt Subspace Theorem to establish the transcendence of a class of quasi-periodic continued fractions. This improves earlier works of Maillet and of A. Baker. We also improve an old result of Davenport and Roth on the rate of increase of the denominators of the convergents to any real algebraic number.

متن کامل

NON-CONVERGING CONTINUED FRACTIONS RELATED TO THE STERN DIATOMIC SEQUENCE by

— This note is essentially an addendum to the recent article of Dilcher and Stolarsky [7] though some results presented here may be of independent interest. We prove the transcendence of some irregular continued fractions which are related to the Stern diatomic sequence. The proofs of our results rest on the so-called Mahler method.

متن کامل

Transcendence measures for continued fractions involving repetitive or symmetric patterns

It was observed long ago (see e.g., [32] or [20], page 62) that Roth’s theorem [28] and its p-adic extension established by Ridout [27] can be used to prove the transcendence of real numbers whose expansion in some integer base contains repetitive patterns. This was properly written only in 1997, by Ferenczi and Mauduit [21], who adopted a point of view from combinatorics on words before applyi...

متن کامل

Metrical Theory for Α-rosen Fractions

Abstract. The Rosen fractions form an infinite family which generalizes the nearestinteger continued fractions. In this paper we introduce a new class of continued fractions related to the Rosen fractions, the α-Rosen fractions. The metrical properties of these α-Rosen fractions are studied. We find planar natural extensions for the associated interval maps, and show that these regions are clos...

متن کامل

Continued fractions with low complexity: Transcendence measures and quadratic approximation

We establish measures of non-quadraticity and transcendence measures for real numbers whose sequence of partial quotients has sublinear block complexity. The main new ingredient is an improvement of Liouville’s inequality giving a lower bound for the distance between two distinct quadratic real numbers. Furthermore, we discuss the gap between Mahler’s exponent w2 and Koksma’s exponent w ∗ 2 .

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010