Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)
Ramification groups and Artin conductors of radical extensions of
We study the ramification properties of the extensions under the hypothesis that is odd and if than either or ( and are the exponents with which divides and ). 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 -adique valuation of the discriminant of the studied global extensions with .
Ramifications minimales
Nous appliquons à la notion d’extension (cyclique de degré ) 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
Ray class fields of global function fields with many rational places
Real quadratic number fields with metacyclic Hilbert -class field tower
We begin by giving a criterion for a number field 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 that have a metacyclic nonabelian Hilbert -class field tower.
Regulators and Iwasawa Modules.
Relations between the values of zeta and L-functions at integral arguments
Representation fields for commutative orders
A representation field for a non-maximal order 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 . 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.
Representation of prime powers in arithmetical progressions by binary quadratic forms
Let be a set of binary quadratic forms of the same discriminant, a set of arithmetical progressions and a positive integer. We investigate the representability of prime powers lying in some progression from by some form from .
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