On a Class of Continued Fractions

نویسندگان

چکیده

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Continued Fractions and Class Number Two

We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm-induced quadratic polynomial. By doing so, this provides a real quadratic field analogue of the well-known result by Hendy (1974) for complex quadratic fields. We illustrate with several example...

متن کامل

On the entropy of Japanese continued fractions

We consider a one-parameter family of expanding interval maps {Tα}α∈[0,1] (japanese continued fractions) which include the Gauss map (α = 1) and the nearest integer and by-excess continued fraction maps (α = 1 2 , α = 0). We prove that the Kolmogorov-Sinai entropy h(α) of these maps depends continuously on the parameter and that h(α) → 0 as α → 0. Numerical results suggest that this convergence...

متن کامل

On the Extremal Theory of Continued Fractions

Letting x = [a1(x), a2(x), . . .] denote the continued fraction expansion of an irrational number x ∈ (0, 1), Khinchin proved that Sn(x) = ∑n k=1 ak(x) ∼ 1 log 2 n logn in measure, but not for almost every x. Diamond and Vaaler showed that removing the largest term from Sn(x), the previous asymptotics will hold almost everywhere, showing the crucial influence of the extreme terms of Sn(x) on th...

متن کامل

Generalized Continued Logarithms and Related Continued Fractions

We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base b. We show that all of our so-called type III continued logarithms converge and all rational numbers have fin...

متن کامل

Continued Logarithms and Associated Continued Fractions

We investigate some of the connections between continued fractions and continued logarithms. We study the binary continued logarithms as introduced by Bill Gosper and explore two generalizations of the continued logarithm to base b. We show convergence for them using equivalent forms of their corresponding continued fractions. Through numerical experimentation we discover that, for one such for...

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

ژورنال

عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society

سال: 1916

ISSN: 0013-0915,1464-3839

DOI: 10.1017/s0013091500029679