Transcendental Continued Fractions over IKp(X)

نویسنده

  • H. Benamar
چکیده

The purpose behind this work is to construct from a family of algebraic formal power series of degree more than 2, a family of transcendental fractions over IKp(X).

برای دانلود رایگان 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

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

Continued fractions and transcendental numbers

It is widely believed that the continued fraction expansion of every irrational algebraic number α either is eventually periodic (and we know that this is the case if and only if α is a quadratic irrational), or it contains arbitrarily large partial quotients. Apparently, this question was first considered by Khintchine in [22] (see also [6,39,41] for surveys including a discussion on this subj...

متن کامل

Curious Continued Fractions, Nonlinear Recurrences, and Transcendental Numbers

We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear interlaced in the continued fraction expansion of the sum of the reciprocals of the terms. Using the rapid (double exponential) growth of the ter...

متن کامل

Palindromic continued fractions

An old problem adressed by Khintchin [15] deals with the behaviour of the continued fraction expansion of algebraic real numbers of degree at least three. In particular, it is asked whether such numbers have or not arbitrarily large partial quotients in their continued fraction expansion. Although almost nothing has been proved yet in this direction, some more general speculations are due to La...

متن کامل

A Short Proof of the Transcendence of Thue-Morse Continued Fractions

The Thue-Morse sequence t = (tn)n≥0 on the alphabet {a, b} is defined as follows: tn = a (respectively, tn = b) if the sum of binary digits of n is even (respectively, odd). This famous binary sequence was first introduced by A. Thue [12] in 1912. It was considered nine years later by M. Morse [7] in a totally different context. These pioneering papers have led to a number of investigations and...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007