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CONTINUED FRACTIONS FOR COMPLEX NUMBERS AND VALUES OF BINARY QUADRATIC FORMS

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Title CONTINUED FRACTIONS FOR COMPLEX NUMBERS AND VALUES OF BINARY QUADRATIC FORMS
 
Creator DANI, SG
NOGUEIRA, A
 
Description We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Such numerous distinct expansions are possible for a complex number. They can be arrived at through various algorithms, as also in a more general way than what we call "iteration sequences". We consider in this broader context the analogues of the Lagrange theorem characterizing quadratic surds, the growth properties of the denominators of the convergents, and the overall relation between sequences satisfying certain conditions, in terms of non-occurrence of certain finite blocks, and the sequences involved in continued fraction expansions. The results are also applied to describe a class of binary quadratic forms with complex coefficients whose values over the set of pairs of Gaussian integers form a dense set of complex numbers.
 
Publisher AMER MATHEMATICAL SOC
 
Date 2014-12-28T10:52:49Z
2014-12-28T10:52:49Z
2014
 
Type Article
 
Identifier TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 366(7)3553-3583
0002-9947
1088-6850
http://dspace.library.iitb.ac.in/jspui/handle/100/16288
 
Language English