Invariants numériques des groupes de Hilbert.
Invariants of a quadratic form attached to a tame covering of schemes
We build on preceeding work of Serre, Esnault-Kahn-Viehweg and Kahn to establish a relation between invariants, in modulo 2 étale cohomology, attached to a tamely ramified covering of schemes with odd ramification indices. The first type of invariant is constructed using a natural quadratic form obtained from the covering. In the case of an extension of Dedekind domains, mains, this form is the square root of the inverse different equipped with the trace form. In the case of a covering of Riemann...
Invariants of number fields related to central embedding problems.
Invariants of the ideal class group and the Hasse norm theorem.
Inverse zero-sum problems in finite Abelian p-groups
We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over...
Investigating generalized quaternions with dual-generalized complex numbers
We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values , and . Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given.
Irreducibility of automorphic Galois representations of , at most
Let be a regular, algebraic, essentially self-dual cuspidal automorphic representation of , where is a totally real field and is at most . We show that for all primes , the -adic Galois representations associated to are irreducible, and for all but finitely many primes , the mod Galois representations associated to are also irreducible. We also show that the Lie algebras of the Zariski closures of the -adic representations are independent of .
Irreducibility of the iterates of a quadratic polynomial over a field
1. Introduction. Let K be a field of characteristic p ≥ 0 and let f(X) be a polynomial of degree at least two with coefficients in K. We set f₁(X) = f(X) and define for all r ≥ 1. Following R. W. K. Odoni [7], we say that f is stable over K if is irreducible over K for every r ≥ 1. In [6] the same author proved that the polynomial f(X) = X² - X + 1 is stable over ℚ. He wrote in [7] that the proof given there is quite difficult and it would be of interest to have an elementary proof. In the sequel...
Irreducible polynomials with all but one zero close to the unit disk
We consider a certain class of polynomials whose zeros are, all with one exception, close to the closed unit disk. We demonstrate that the Mahler measure can be employed to prove irreducibility of these polynomials over ℚ.
Irreducible polynomials with many roots of maximal modulus
Irregular imaginary fields
Isomorphisms of algebraic number fields
Let and be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, . The algorithm is particularly efficient if there is only one isomorphism.
Iterated Ring Class Fields and the 168-Tesselation.
Iterated Ring Class Fields and the Icosahedron.
Itération de polynômes et fonctions entières arithmétiques
Iwasawa algebras and arithmetic
Iwasawa Invariants.
Iwasawa Invariants of Abelian Number Fields.
Iwasawa invariants of imaginary quadratic fields.
Iwasawa L-Functions of Varieties over Algebraic Number Fields.