Führer, Diskriminante und Verzweigungskörper relativ-Abelscher Zahlkörper.
Function fields with 3-rank at least 2
Function fields with class number indivisible by a prime ℓ
Galois module structure of units in real biquadratic number fields
Galois representations of Iwasawa modules
Galois-Cohen-Lenstra heuristics
Generalization of a theorem of Siegel
Generalized Lagrange criteria for certain quadratic Diophantine equations.
Global restrictions on ramification in number fields.
Governing fields for the 2-classgroup of and a related reciprocity law
Gross’ conjecture for extensions ramified over four points of
In this paper, under a mild hypothesis, we prove a conjecture of Gross for the Stickelberger element of the maximal abelian extension over the rational function field unramified outside a set of four degree-one places.
Hasse's Class Number Product Formula for Generalized Dirichlet Fields and other types of Number Fields.
Hasse’s problem for monogenic fields
In this article we shall give a survey of Hasse’s problem for integral power bases of algebraic number fields during the last half of century. Specifically, we developed this problem for the abelian number fields and we shall show several substantial examples for our main theorem [7] [9], which will indicate the actual method to generalize for the forthcoming theme on Hasse’s problem [15].
Heckesche Systeme idealer Zahlen und Knesersche Körpererweiterungen
Einleitung. Eine klassische Konstruktion aus der algebraischen Zahlentheorie ist folgende: Zu jedem algebraischen Zahlkörper K kann man ein sogenanntes System idealer Zahlen S zuordnen, welches eine Untergruppe der multiplikativen Gruppe ℂ* der komplexen Zahlen ist derart, daß die Faktorgruppe S/K* in kanonischer Weise isomorph zu der Klassengruppe von K ist. Diese Konstruktion geht auf Hecke [5] zurück und hat folgende wichtige Eigenschaft, die auch bei dem Hilbertschen Klassenkörper zu K vorkommt:...
Heuristics on Tate-Shafarevitch groups of elliptic curves defined over .
Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a -adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good.
Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves
We study the problem of constructing and enumerating, for any integers , number fields of degree whose ideal class groups have “large" -rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.
Ideal Class Groups in Basic ...p1 x....x...ps-Extensions of Abelian Number Fields.
Ideal class groups of cubic cyclic fields
Ideal class groups of cyclotomic number fields I