Periodic continued fractions and Kronecker symbols
Number Theory
2015-04-13 v1
Abstract
We study the Kronecker symbol for the sequence of the convergents of a purely periodic continued fraction expansion. Whereas the corresponding sequence of Jacobi symbols is always periodic, it turns out that the sequence of Kronecker symbols may be aperiodic. Our main result describes the period length in the periodic case in terms of the period length of the sequence of Jacobi symbols and gives a necessary and sufficient condition for the occurrence of the aperiodic case.
Keywords
Cite
@article{arxiv.1504.02618,
title = {Periodic continued fractions and Kronecker symbols},
author = {Kurt Girstmair},
journal= {arXiv preprint arXiv:1504.02618},
year = {2015}
}