Continued fractions

The study of continued fractions is an ancient part of elementary Number Theory. It was studied by Leonhard Euler in the 18-th century. Actually, a remarkable paper from him was translated from Latin language into English and published thirty years ago [1]. The subject has been treated very deeply by Oskar Perron at the beginning of the 20 th century, in a famous book which has been edited several times [2]. It can also be found in several books on Number Theory, among them a famous one is “An Introduction to the Theory of Numbers” due to Hardy and Wright which was reedited many times until recently [3].

[1]  A. Lasjaunias.  A Survey of Diophantine Approximationin Fields of Power Series , 2000 .

[2]  W. Schmidt.  On continued fractions and diophantine approximation in power series fields , 2000 .

[3]  A. Lasjaunias.  Diophantine Approximation and Continued Fraction Expansions of Algebraic Power Series in Positive Characteristic , 1997 .

[4]  D. P. Robbins,et al.  The Continued Fraction Expansion of An Algebraic Power Series Satisfying A Quartic Equation , 1995 .

[5]  W. Gruyter,et al.  Thue's Theorem in positive characteristic. , 1995 .

[6]  Robert M Corless.  Continued fractions and chaos , 1992 .

[7]  Claude Brezinski,et al.  History of continued fractions and Pade approximants , 1990, Springer series in computational mathematics.

[8]  W. H. Mills,et al.  Continued fractions for certain algebraic power series , 1986 .

[9]  L. Baum,et al.  Badly approximable power series in characteristic 2 , 1977 .

[10]  L. Baum,et al.  Continued fractions of algebraic power series in characteristic 2 , 1976 .

[11]  L. Euler.  On Continued Fractions , 1972 .

[12]  M. Kline.  Mathematical Thought from Ancient to Modern Times , 1972 .

[13]  Ralph G. Archibald,et al.  An introduction to the theory of numbers , 1970 .

[14]  K. Mahler.  On a Theorem of Liouville in Fields of Positive Characteristic , 1949, Canadian Journal of Mathematics.

[15]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.

[16]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.