Displaying similar documents to “Consecutive powers in continued fractions”

Even partition functions.

Ben Saïd, F., Nicolas, J.-L. (2002)

Séminaire Lotharingien de Combinatoire [electronic only]

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A note on codes and kets.

Caragiu, Mihai (2005)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Jacobi symbols, ambiguous ideals, and continued fractions

R. A. Mollin (1998)

Acta Arithmetica

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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.

Length of continued fractions in principal quadratic fields

Guillaume Grisel (1998)

Acta Arithmetica

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Let d ≥ 2 be a square-free integer and for all n ≥ 0, let l ( ( √ d ) 2 n + 1 ) be the length of the continued fraction expansion of ( √ d ) 2 n + 1 . If ℚ(√d) is a principal quadratic field, then under a condition on the fundamental unit of ℤ[√d] we prove that there exist constants C₁ and C₂ such that C ₁ ( √ d ) 2 n + 1 ≥ l ( ( √ d ) 2 n + 1 ) ≥ C ₂ ( √ d ) 2 n + 1 for all large n. This is a generalization of a theorem of S. Chowla and S. S. Pillai [2] and an improvement in a particular case of a theorem of [6].