Jacobi symbols, ambiguous ideals, and continued fractions

• Autorzy: R. A. Mollin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11R11: Quadratic extensions
• 11R65: Class groups and Picard groups of orders
• 11R29: Class numbers, class groups, discriminants
• 11D09: Quadratic and bilinear equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 4
• Strony: 331-349

Daty

wydano

1998

otrzymano

1997-07-30

poprawiono

1997-12-15

Twórcy

autor

R. A. Mollin

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

Bibliografia

• [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.