Displaying similar documents to “The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields”

Shift spaces and attractors in noninvertible horseshoes

H. Bothe (1997)

Fundamenta Mathematicae

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As is well known, a horseshoe map, i.e. a special injective reimbedding of the unit square I 2 in ℝ 2 (or more generally, of the cube I m in ℝ m ) as considered first by S. Smale [5], defines a shift dynamics on the maximal invariant subset of I 2 (or I m ). It is shown that this remains true almost surely for noninjective maps provided the contraction rate of the mapping in the stable direction is sufficiently strong, and bounds for this rate are given.

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].

The Iwasawa λ-invariants of ℤₚ-extensions of real quadratic fields

Takashi Fukuda, Hisao Taya (1995)

Acta Arithmetica

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1. Introduction. Let k be a totally real number field. Let p be a fixed prime number and ℤₚ the ring of all p-adic integers. We denote by λ=λₚ(k), μ=μₚ(k) and ν=νₚ(k) the Iwasawa invariants of the cyclotomic ℤₚ-extension k ∞ of k for p (cf. [10]). Then Greenberg’s conjecture states that both λₚ(k) and μₚ(k) always vanish (cf. [8]). In other words, the order of the p-primary part of the ideal class group of kₙ remains bounded as n tends to infinity, where kₙ is the nth layer of k ∞ / k . We know...

On strong uniform distribution, II. The infinite-dimensional case

Y. Lacroix (1998)

Acta Arithmetica

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We construct infinite-dimensional chains that are L¹ good for almost sure convergence, which settles a question raised in this journal [N]. We give some conditions for a coprime generated chain to be bad for L² or L ∞ , using the entropy method. It follows that such a chain with positive lower density is bad for L ∞ . There also exist such bad chains with zero density.

The relative coincidence Nielsen number

Jerzy Jezierski (1996)

Fundamenta Mathematicae

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We define a relative coincidence Nielsen number N r e l ( f , g ) for pairs of maps between manifolds, prove a Wecken type theorem for this invariant and give some formulae expressing N r e l ( f , g ) by the ordinary Nielsen numbers.

Embedding lattices in the Kleene degrees

Hisato Muraki (1999)

Fundamenta Mathematicae

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Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed ℵ 1 can be embedded in some local structures of Kleene degrees.