Governing fields for the 2-classgroup of $Q(sqrt{-q_{1}q_{2}p})$ and a related reciprocity law

Patrick Morton

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Displaying similar documents to “Governing fields for the 2-classgroup of $Q (s q r t - q_{1} q_{2} p)$ and a related reciprocity law”

On divisibility of $h^{+}$ by the prime $5$

Stanislav Jakubec (1994)

Mathematica Slovaca

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$H^{p}$ -spaces of conjugate systems on local fields

Jia Chao (1974)

Studia Mathematica

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On some imaginary triquadratic number fields $k$ with ${Cl}_{2} (k) ≃ (2, 4)$ or $(2, 2, 2)$

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2021)

Commentationes Mathematicae Universitatis Carolinae

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Let $d$ be a square free integer and $L_{d} : = ℚ (ζ_{8}, \sqrt{d})$ . In the present work we determine all the fields $L_{d}$ such that the $2$ -class group, ${Cl}_{2} (L_{d})$ , of $L_{d}$ is of type $(2, 4)$ or $(2, 2, 2)$ .

Isomorphisms of algebraic number fields

Mark van Hoeij, Vivek Pal (2012)

Journal de Théorie des Nombres de Bordeaux

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Let $ℚ (α)$ and $ℚ (β)$ be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, $ℚ (β) \to ℚ (α)$ . The algorithm is particularly efficient if there is only one isomorphism.

Unit vector fields on antipodally punctured spheres: big index, big volume

Fabiano G. B. Brito, Pablo M. Chacón, David L. Johnson (2008)

Bulletin de la Société Mathématique de France

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We establish in this paper a lower bound for the volume of a unit vector field $\vec{v}$ defined on $𝐒^{n} ∖ {\pm x}$ , $n = 2, 3$ . This lower bound is related to the sum of the absolute values of the indices of $\vec{v}$ at $x$ and $- x$ .

A remark on the transport equation with b ∈ BV and $d i v_{x} b \in B M O$

Paweł Subko (2014)

Colloquium Mathematicae

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We investigate the transport equation $\partial_{t} u (t, x) + b (t, x) \cdot D_{x} u (t, x) = 0$ . Our result improves the classical criteria of uniqueness of weak solutions in the case of irregular coefficients: b ∈ BV, $d i v_{x} b \in B M O$ . To obtain our result we use a procedure similar to DiPerna and Lions’s one developed for Sobolev vector fields. We apply renormalization theory for BV vector fields and logarithmic type inequalities to obtain energy estimates.

On the $2$ -class group of some number fields with large degree

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini (2021)

Archivum Mathematicum

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Let $d$ be an odd square-free integer, $m \geq 3$ any integer and $L_{m, d} : = ℚ (ζ_{2^{m}}, \sqrt{d})$ . In this paper, we shall determine all the fields $L_{m, d}$ having an odd class number. Furthermore, using the cyclotomic $ℤ_{2}$ -extensions of some number fields, we compute the rank of the $2$ -class group of $L_{m, d}$ whenever the prime divisors of $d$ are congruent to $3$ or $5 (mod 8)$ .

Principalization algorithm via class group structure

Daniel C. Mayer (2014)

Journal de Théorie des Nombres de Bordeaux

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For an algebraic number field $K$ with $3$ -class group ${Cl}_{3} (K)$ of type $(3, 3)$ , the structure of the $3$ -class groups ${Cl}_{3} (N_{i})$ of the four unramified cyclic cubic extension fields $N_{i}$ , $1 \leq i \leq 4$ , of $K$ is calculated with the aid of presentations for the metabelian Galois group $G_{3}^{2} (K) = Gal (F_{3}^{2} (K) | K)$ of the second Hilbert $3$ -class field $F_{3}^{2} (K)$ of $K$ . In the case of a quadratic base field $K = ℚ (\sqrt{D})$ it is shown that the structure of the $3$ -class groups of the four $S_{3}$ -fields $N_{1}, ..., N_{4}$ frequently determines the type of principalization of the $3$ -class group of $K$ in $N_{1}, ..., N_{4}$ . This...

An explicit computation of $p$ -stabilized vectors

Michitaka MIYAUCHI, Takuya YAMAUCHI (2014)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we give a concrete method to compute $p$ -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over $p$ -adic fields. An application to the global setting is also discussed. In particular, we give an explicit $p$ -stabilized form of a Saito-Kurokawa lift.

The natural operators $T_{| ℳ f ₙ} ⇝ T * T^{r }$ and $T_{| ℳ f ₙ} ⇝ Λ ² T T^{r *}$

W. M. Mikulski (2002)

Colloquium Mathematicae

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Let r and n be natural numbers. For n ≥ 2 all natural operators $T_{| ℳ f ₙ} ⇝ T * T^{r *}$ transforming vector fields on n-manifolds M to 1-forms on $T^{r *} M = J^{r} (M, ℝ) ₀$ are classified. For n ≥ 3 all natural operators $T_{| ℳ f ₙ} ⇝ Λ ² T * T^{r *}$ transforming vector fields on n-manifolds M to 2-forms on $T^{r *} M$ are completely described.