Jacobi symbols, ambiguous ideals, and continued fractions
Acta Arithmetica (1998)
- Volume: 85, Issue: 4, page 331-349
- ISSN: 0065-1036
Access Full Article
top
Abstract
topHow to cite
topR. A. Mollin. "Jacobi symbols, ambiguous ideals, and continued fractions." Acta Arithmetica 85.4 (1998): 331-349. <http://eudml.org/doc/207173>.
@article{R1998,
abstract = {The purpose of this paper is to generalize some seminal results in the literature concerning the interrelationships between Legendre symbols and continued fractions. We introduce the power of ideal theory into the arena. This allows significant improvements over the existing results via the infrastructure of real quadratic fields.},
author = {R. A. Mollin},
journal = {Acta Arithmetica},
keywords = {ambiguous ideals; Legendre symbols; Jacobi symbols; continued fractions; real quadratic fields; Richaud-Degert fields},
language = {eng},
number = {4},
pages = {331-349},
title = {Jacobi symbols, ambiguous ideals, and continued fractions},
url = {http://eudml.org/doc/207173},
volume = {85},
year = {1998},
}
TY - JOUR
AU - R. A. Mollin
TI - Jacobi symbols, ambiguous ideals, and continued fractions
JO - Acta Arithmetica
PY - 1998
VL - 85
IS - 4
SP - 331
EP - 349
AB - The purpose of this paper is to generalize some seminal results in the literature concerning the interrelationships between Legendre symbols and continued fractions. We introduce the power of ideal theory into the arena. This allows significant improvements over the existing results via the infrastructure of real quadratic fields.
LA - eng
KW - ambiguous ideals; Legendre symbols; Jacobi symbols; continued fractions; real quadratic fields; Richaud-Degert fields
UR - http://eudml.org/doc/207173
ER -
References
top- [1] P. Chowla and S. Chowla, Problems on periodic simple continued fractions, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 3745. Zbl0247.10019
- [2] H. Cohn, A Second Course in Number Theory, Wiley, New York, 1962.
- [3] C. Friesen, Legendre symbols and continued fractions, Acta Arith. 59 (1991), 365-379. Zbl0706.11004
- [4] R. A. Mollin, Quadratics, CRC Press, Boca Raton, 1995.
- [5] A. Schinzel, On two conjectures of P. Chowla and S. Chowla concerning continued fractions, Ann. Mat. Pura Appl. 98 (1974), 111-117. Zbl0281.10013
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.