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Displaying 21 – 37 of 37

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

Takashi Fukuda, Hisao Taya (1995)

Acta Arithmetica

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 $k_{\infty}$ 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 $k_{\infty} / k$ . We know by the Ferrero-Washington...

The number of real quadratic fields having units of negative norm.

Stevenhagen, Peter (1993)

Experimental Mathematics

The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders

Richard A. Mollin (1995)

Journal de théorie des nombres de Bordeaux

Herein we introduce the palindromic index as a device for studying ambiguous cycles of reduced ideals with no ambiguous ideal in the cycle.

The size of the fundamental solutions of consecutive Pell equations.

Jacobson, Michael J.jun., Williams, Hugh C. (2000)

Experimental Mathematics

The Stickelberger element of an imaginary quadratic field

Peter Schmid (1999)

Acta Arithmetica

The structure of the tame kernels of quadratic number fields (II)

Xiaobin Yin, Hourong Qin, Qunsheng Zhu (2005)

Acta Arithmetica

The structure of the tame kernels of quadratic number fields (I)

H. R. Qin (2004)

Acta Arithmetica

The universality theorem for class group L-functions

Hidehiko Mishou (2011)

Acta Arithmetica

Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper.

Carl Friedrich Hermann (1987)

Mathematische Annalen

Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper. II.

Carl Friedrich Hermann (1989)

Mathematische Annalen

Torsion groups of elliptic curves with integral j-invariant over quadratic fields.

H.H. Müller, H. Ströher, H.G. Zimmer (1989)

Journal für die reine und angewandte Mathematik

Torsion points on elliptic curves over all quadratic fields. II

Sheldon Kamienny (1986)

Bulletin de la Société Mathématique de France

Torsion points on elliptic curves over fileds of low degree.

S. Kamienny (1989)

Manuscripta mathematica

Towards Bauer's theorem for linear recurrence sequences

Mariusz Skałba (2003)

Colloquium Mathematicae

Consider a recurrence sequence ${(x_{k})}_{k \in ℤ}$ of integers satisfying $x_{k + n} = a_{n - 1} x_{k + n - 1} + . . . + a ₁ x_{k + 1} + a ₀ x_{k}$ , where $a ₀, a ₁, . . ., a_{n - 1} \in ℤ$ are fixed and a₀ ∈ -1,1. Assume that $x_{k} > 0$ for all sufficiently large k. If there exists k₀∈ ℤ such that $x_{k ₀} < 0$ then for each negative integer -D there exist infinitely many rational primes q such that $q | x_{k}$ for some k ∈ ℕ and (-D/q) = -1.

Currently displaying 21 – 37 of 37

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Displaying 21 – 37 of 37

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

The number of real quadratic fields having units of negative norm.

The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders

The size of the fundamental solutions of consecutive Pell equations.

The Stickelberger element of an imaginary quadratic field

The structure of the tame kernels of quadratic number fields (II)

The structure of the tame kernels of quadratic number fields (I)

The universality theorem for class group L-functions

Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper.

Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper. II.

Torsion groups of elliptic curves with integral j-invariant over quadratic fields.

Torsion points on elliptic curves over all quadratic fields. II

Torsion points on elliptic curves over fileds of low degree.

Towards Bauer's theorem for linear recurrence sequences

Trace formulae and imaginary quadratic fields.

Travaux de Coates et Wiles sur la conjecture de Birch et Swinnerton-Dyer

Twists of the Iwasawa-Tate Zeta Function.

Currently displaying 21 – 37 of 37