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Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves

Aaron Levin (2007)

Journal de Théorie des Nombres de Bordeaux

We study the problem of constructing and enumerating, for any integers $m, n > 1$ , number fields of degree $n$ whose ideal class groups have “large" $m$ -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.

Eduardo C. Friedmann (1981/1982)

Inventiones mathematicae

Ideal class groups of cubic cyclic fields

Shin Nakano (1986)

Acta Arithmetica

Ideal class groups of cyclotomic number fields I

Franz Lemmermeyer (1995)

Acta Arithmetica

Ideal class groups of cyclotomic number fields II

Franz Lemmermeyer (1998)

Acta Arithmetica

Ideal class groups of cyclotomic number fields III

Franz Lemmermeyer (2008)

Acta Arithmetica

Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung.

Rainer Zimmert (1980/1981)

Inventiones mathematicae

Imaginäre quadratische Zahlkörper mit der Klassenzahl l .

M. Deuring (1933)

Mathematische Zeitschrift

Imaginary quadratic fields with small odd class number

Steven Arno, M. L. Robinson, Ferrell S. Wheeler (1998)

Acta Arithmetica

Inclusion of CM-fields and divisibility ofrelative class numbers

Ryotaro Okazaki (2000)

Acta Arithmetica

Index for subgroups of the group of units in number fields

Tsutomu Shimada (1998)

Acta Arithmetica

We define a sequence of rational integers $u_{i} (E)$ for each finite index subgroup E of the group of units in some finite Galois number fields K in which prime p ramifies. For two subgroups E’ ⊂ E of finite index in the group of units of K we prove the formula $v_{p} ([E : E^{'}]) = \sum_{i = 1}^{r} u_{i} (E^{'}) - u_{i} (E)$ . This is a generalization of results of P. Dénes [3], [4] and F. Kurihara [5].

Currently displaying 1 – 20 of 23

Page 1 Next

Displaying 1 – 20 of 23

Ideal class groups, Hilbert’s irreducibility theorem, and 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

Ideal class groups of cyclotomic number fields II

Ideal class groups of cyclotomic number fields III

Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung.

Imaginäre quadratische Zahlkörper mit der Klassenzahl l .

Imaginary quadratic fields with small odd class number

Inclusion of CM-fields and divisibility ofrelative class numbers

Index for subgroups of the group of units in number fields

Indivisibility of class numbers of global function fields

Indivisibility of class numbers of imaginary quadratic function fields

Indivisibility of class numbers of real quadratic fields.

Indivisibility of special values of Dedekind zeta functions of real quadratic fields

Inégalités de miroir

Infinite 2-class field towers of some imaginary quadratic number fields

Infinite Hilbert 2-class field tower of quadratic number fields

Inmersiones de órdenes cuadráticos en el orden generador por T^iN).

Integral points of a modular curve of level 11

Currently displaying 1 – 20 of 23