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ArticleOriginal scientific text

Title

Jacobi symbols, ambiguous ideals, and continued fractions

Authors 1

Affiliations

  1. Mathematics Department, University of Calgary, Calgary, Alberta, Canada, T2N 1N4

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.

Bibliography

  1. P. Chowla and S. Chowla, Problems on periodic simple continued fractions, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 3745.
  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.
  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.
Acta Arithmetica
1998/85/4
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Pages:
331-349
Main language of publication
English
Received
1997-07-30
Accepted
1997-12-15
Published
1998
Exact and natural sciences