Continued fractions and class number two.

Mollin, Richard A.

Displaying similar documents to “Continued fractions and class number two.”

Solvability of nonlinear Hammerstein quadratic integral equations.

El-Sayed, A.M.A., Hashem, H.H.G. (2009)

The Journal of Nonlinear Sciences and its Applications

Similarity:

Ramanujan's evaluations of Rogers-Ramanujan type continued fractions at primitive roots of unity

Sen-Shan Huang (1997)

Acta Arithmetica

Similarity:

Weyl sequences: Asymptotic distributions of the partition lengths

Anatoly Zhigljavsky, Iskander Aliev (1999)

Acta Arithmetica

Similarity:

Length of continued fractions in principal quadratic fields

Guillaume Grisel (1998)

Acta Arithmetica

Similarity:

Let d ≥ 2 be a square-free integer and for all n ≥ 0, let $l ({(\sqrt d)}^{2 n + 1})$ be the length of the continued fraction expansion of ${(\sqrt d)}^{2 n + 1}$ . 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 $C ₁ {(\sqrt d)}^{2 n + 1} \geq l ({(\sqrt d)}^{2 n + 1}) \geq C ₂ {(\sqrt d)}^{2 n + 1}$ 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].

An improved upper bound for the discrepancy of quadratic congruential pseudorandom numbers

Jürgen Eichenauer-Herrmann, Harald Niederreiter (1995)

Acta Arithmetica

Similarity:

Convergents of folded continued fractions

Jean-Paul Allouche, Anna Lubiw, Michel Mendès France, Alfred J. van der Poorten, Jeffrey Shallit (1996)

Acta Arithmetica

Similarity:

Minimum and maximum order of magnitude of the discrepancy of (nα)

C. Baxa, J. Schoissengeier (1994)

Acta Arithmetica

Similarity:

On Ramanujan's cubic continued fraction

Heng Huat Chan (1995)

Acta Arithmetica

Similarity:

Note on the congruence of Ankeny-Artin-Chowla type modulo p²

Stanislav Jakubec (1998)

Acta Arithmetica

Similarity:

The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of $ℚ (ζ_{p})$ of a prime degree l is simplified. This is done on the basis of a congruence for the Gauss period (Theorem 1). The results are applied for the quadratic field ℚ(√p), p ≡ 5 (mod 8) (Corollary 1).