Infinite-dimensional generalized continued fractions, quadratic residues and non-residues, and ergodic theory

1997 ◽  
Vol 52 (2) ◽  
pp. 420-421 ◽  
Author(s):  
L D Pustyl'nikov
Keyword(s):  
Ergodic Theory ◽  
Continued Fractions ◽  
Infinite Dimensional ◽  
Quadratic Residues ◽  
Generalized Continued Fractions

INFINITE-DIMENSIONAL GENERALIZED CONTINUED FRACTIONS, DISTRIBUTION OF QUADRATIC RESIDUES AND NON-RESIDUES, AND ERGODIC THEORY

2002 ◽  
Vol 05 (04) ◽  
pp. 555-570
Author(s):  
L. D. PUSTYL'NIKOV
Keyword(s):  
Prime Number ◽  
Ergodic Theory ◽  
Continued Fractions ◽  
Classical Problem ◽  
Infinite Dimensional ◽  
Ergodic Properties ◽  
Quadratic Residues ◽  
Generalized Continued Fractions

A new theory of generalized continued fractions for infinite-dimensional vectors with integer components is constructed. The results of this theory are applied to the classical problem on the distribution of quadratic residues and non-residues modulo a prime number and are based on the study of ergodic properties of some infinite-dimensional transformations.

Markov chains and generalized continued fractions

1992 ◽  
Vol 29 (04) ◽  
pp. 838-849 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Wide Class ◽  
Stochastic Models ◽  
Continuous Time ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Continuous Time Markov Chains ◽  
Generalized Continued Fractions

This paper deals with a class of discrete-time Markov chains for which the invariant measures can be expressed in terms of generalized continued fractions. The representation covers a wide class of stochastic models and is well suited for numerical applications. The results obtained can easily be extended to continuous-time Markov chains.

scholarly journals On irrationality exponents of generalized continued fractions

2015 ◽  
Vol 151 ◽  
pp. 18-35 ◽  
Author(s):  
Jaroslav Hančl ◽  
Kalle Leppälä ◽  
Tapani Matala-aho ◽  
Topi Törmä
Keyword(s):  
Continued Fractions ◽  
Generalized Continued Fractions
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