Independent systems of units in certain algebraic number fields.
Index for subgroups of the group of units in number fields
We define a sequence of rational integers 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 . This is a generalization of results of P. Dénes [3], [4] and F. Kurihara [5].
Index form equations in quintic fields
The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]), every index form equation can be reduced to an equation system consisting of unit equations in two variables over the normal closure of the original field. However, the unit rank of the normal closure is usually too large for practical use. In a recent paper Győry [27] succeeded in reducing index form equations to systems of unit...
Index of irregularity of a prime.
Indice des unités elliptiques dans les -extensions
Nous comparons le comportement dans les -extensions du nombre de classes d’idéaux avec le comportement de l’indice du groupe des unités elliptiques de Rubin.
Indices of subfields of cyclotomic ℤₚ-extensions and higher degree Fermat quotients
We consider the indices of subfields of cyclotomic ℤₚ-extensions of number fields. For the nth layer Kₙ of the cyclotomic ℤₚ-extension of ℚ, we find that the prime factors of the index of Kₙ/ℚ are those primes less than the extension degree pⁿ which split completely in Kₙ. Namely, the prime factor q satisfies , and this leads us to consider higher degree Fermat quotients. Indices of subfields of cyclotomic ℤₚ-extensions of a number field which is cyclic over ℚ with extension degree a prime different...
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
Inégalités sur la mesure de Mahler d'un polynôme
Dans cet article, nous donnons une minoration de la mesure de Mahler d'un polynôme à coefficients entiers, dont toutes les racines sont d'une part réelles positives, d'autre part réelles, en fonction de la valeur de ce polynôme en zéro. Ces minorations améliorent des résultats antérieurs de A. Schinzel. Par ailleurs, nous en déduisons des inégalités de M.-J. Bertin, liant la mesure d'un nombre algébrique à sa norme.
Inequalities on polynomial heights.
Infinite 2-class field towers of some imaginary quadratic number fields
Infinite class field towers of quadratic fields.
Infinite Hilbert 2-class field tower of quadratic number fields
Infinite product representations in complex quadratic fields
Infinitely ramified Galois representations.
Inflationary tilings with a similarity structure.
Inhomogeneous norm form equations over function fields