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Displaying 1 – 14 of 14

Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)

Liang-Cheng Zhang (1997)

Acta Arithmetica

Ramification groups and Artin conductors of radical extensions of $ℚ$

Filippo Viviani (2004)

Journal de Théorie des Nombres de Bordeaux

We study the ramification properties of the extensions $ℚ (ζ_{m}, \sqrt[m]{a}) / ℚ$ under the hypothesis that $m$ is odd and if $p ∣ m$ than either $p ∤ v_{p} (a)$ or $p^{v_{p} (m)} ∣ v_{p} (a)$ ( $v_{p} (a)$ and $v_{p} (m)$ are the exponents with which $p$ divides $a$ and $m$ ). In particular we determine the higher ramification groups of the completed extensions and the Artin conductors of the characters of their Galois group. As an application, we give formulas for the $p$ -adique valuation of the discriminant of the studied global extensions with $m = p^{r}$ .

Ramifications minimales

Georges Gras (2000)

Journal de théorie des nombres de Bordeaux

Nous appliquons à la notion d’extension (cyclique de degré $p$ ) à ramification minimale, les techniques de “ réflexion ” qui permettent une caractérisation très simple de ces extensions à l’aide d’un corps gouvernant.

Ranks of 3-class groups of non-Galois cubic fields

Frank Gerth (1976)

Acta Arithmetica

Ray class fields of global function fields with many rational places

Roland Auer (2000)

Acta Arithmetica

Real quadratic number fields with metacyclic Hilbert $2$ -class field tower

Said Essahel, Ahmed Dakkak, Ali Mouhib (2019)

Mathematica Bohemica

We begin by giving a criterion for a number field $K$ with 2-class group of rank 2 to have a metacyclic Hilbert 2-class field tower, and then we will determine all real quadratic number fields $ℚ (\sqrt{d})$ that have a metacyclic nonabelian Hilbert $2$ -class field tower.

Regulators and Iwasawa Modules.

Benedict H. Gross, Federer Leslie J. (1980/1981)

Inventiones mathematicae

Relations between the values of zeta and L-functions at integral arguments

Emil Grosswald (1973)

Acta Arithmetica

Representation fields for commutative orders

Luis Arenas-Carmona (2012)

Annales de l’institut Fourier

A representation field for a non-maximal order $ℌ$ in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of $ℌ$ . Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.

Representation of a prime as the sum of squares in a tower of fields.

Harvey Cohn (1985)

Journal für die reine und angewandte Mathematik

Representation of prime powers in arithmetical progressions by binary quadratic forms

Franz Halter-Koch (2003)

Journal de théorie des nombres de Bordeaux

Let $Γ$ be a set of binary quadratic forms of the same discriminant, $Δ$ a set of arithmetical progressions and $m$ a positive integer. We investigate the representability of prime powers $p^{m}$ lying in some progression from $Δ$ by some form from $Γ$ .

Currently displaying 1 – 14 of 14

Page 1

Displaying 1 – 14 of 14

Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)

Ramification groups and Artin conductors of radical extensions of $ℚ$

Ramifications minimales

Ranks of 3-class groups of non-Galois cubic fields

Ray class fields of global function fields with many rational places

Real quadratic number fields with metacyclic Hilbert $2$ -class field tower

Regulators and Iwasawa Modules.

Relations between the values of zeta and L-functions at integral arguments

Representation fields for commutative orders

Representation of a prime as the sum of squares in a tower of fields.

Representation of prime powers in arithmetical progressions by binary quadratic forms

Representation of primes by the principal form of discriminant -D when the classnumber h(-D) is 3

Résultats récents sur la monogénéité de certains anneaux d'entiers

Résultats sur la théorie des corps de classe

Currently displaying 1 – 14 of 14