Continued fractions for complex numbers and values of binary quadratic forms

Details Continued fractions for complex numbers and values of binary quadratic forms Continued fractions for complex numbers and values of binary quadratic forms

2011-02-18

arxiv.org/abs/1102.3754v1

Mathematics

Number Theory

34 pages, 2 figures

Scientific paper

We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as also in a more general way from 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 nonoccurrence 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.

Affiliated with

Also associated with

No associations

Rating

Continued fractions for complex numbers and values of binary quadratic forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Continued fractions for complex numbers and values of binary quadratic forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continued fractions for complex numbers and values of binary quadratic forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-211482