Search results for: Roberto Dvornicich

Items from 1 to 18 out of 18 results

article

Composite factors of binomials and linear systems in roots of unity

Roberto Dvornicich, Umberto Zannier

Israel Journal of Mathematics > 2019 > 229 > 1 > 381-391

In this paper we completely classify binomials in one variable which have a nontrivial factor which is composite, i.e., of the shape g(h(x)) for polynomials g, h both of degree > 1. In particular, we prove that, if a binomial has such a composite factor, then deg g ≤ 2 (under natural necessary conditions). This is best-possible and improves on a previous bound deg g ≤ 24.This result provides evidence...

article

Finite groups of units of finite characteristic rings

Ilaria Del Corso, Roberto Dvornicich

Annali di Matematica Pura ed Applicata ( 01923 -) > 2018 > 197 > 3 > 661-671

Fuchs (Abelian groups, Pergamon, Oxford, 1960, Problem 72) asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases. The aim of the present paper is to address Fuchs’ question when A is a finite characteristic ring. The result is a pretty good description of the groups...

article

On wild extensions of a p-adic field

Ilaria Del Corso, Roberto Dvornicich, Maurizio Monge

Journal of Number Theory > 2017 > 174 > C > 322-342

In this paper we consider the problem of classifying the isomorphism classes of extensions of degree pk of a p-adic field K, restricting to the case of extensions without intermediate fields.We establish a correspondence between the isomorphism classes of these extensions and some Kummer extensions of a suitable field F containing K. We then describe such classes in terms of the representations of...

chapter

Newton symmetric functions and the arithmetic of algebraically closed fields

Roberto Dvornicich, Carlo Traverso

Lecture Notes in Computer Science > Applied Algebra, Algebraic Algorithms and Error-Correcting Codes > 216-224

In this paper we analyze some points regarding computations on algebraically closed fields. We give an explicit formula for the computation of a polynomial whose roots are the sum (resp. the product) of the roots of two given polynomials. This formula is obtained considering a transformation sending a polynomial in the sequence of its Newton symmetric functions, and allows to obtain a better...

article

The Compositum of Wild Extensions of Local Fields of Prime Degree

Ilaria Del Corso, Roberto Dvornicich

Monatshefte für Mathematik > 2007 > 150 > 4 > 271-288

. In this paper we present a general view of the totally and wildly ramified extensions of degree p of a p-adic field K. Our method consists in deducing the properties of the set of all extensions of degree p of K from the study of the compositum ${\cal C}_K(p)$ of all its elements. We show that in fact ${\cal C}_K(p)$ is the maximal abelian extension of exponent p of F = F(K), where F is...

article

An equivalence between local fields

Ilaria Del Corso, Roberto Dvornicich

Journal of Number Theory > 2005 > 115 > 2 > 230-248

The p-component of the index of a number field K depends only on the completions of K at the primes over p. In this paper we define an equivalence relation between m-tuples of local fields such that, if two number fields K and K′ have equivalent m-tuples of completions at the primes over p, then they have the same p-component of the index. This equivalence can be interpreted in terms of the decomposition...

article

Decomposition of primes in non-maximal orders

Ilaria Del Corso, Roberto Dvornicich, Denis Simon

Acta Arithmetica > 2005 > 120 > 3 > 231-244

article

Un analogue pour les courbes elliptiques de l'exemple de Grunwald-Wang

Roberto Dvornicich, Umberto Zannier

Comptes rendus - Mathematique > 2004 > 338 > 1 > 47-50

We give examples of elliptic curves E/Q and rational points P E(Q) such that P is divisible by 4 in E(Q _v ) for each rational place v but P is not divisible by 4 in E(Q). This is an analogue of a well-known example, with G _m in place of E: namely, P=16 is a rational 8-th power locally almost everywhere, but not globally in Q ^* =G _m (Q). To cite this article: R. Dvornicich,...

article

On polynomials taking small values at integral arguments II

Roberto Dvornicich, Shih Tung, Umberto Zannier

Acta Arithmetica > 2003 > 106 > 2 > 115-121

article

Lower Bounds for the Height and Size of the Ideal Class Group in CM-Fields

Francesco Amoroso, Roberto Dvornicich

Monatshefte für Mathematik > 2003 > 138 > 2 > 85-94

Abstract.We prove that, under the assumption of the Generalized Riemann Hypothesis, the exponent of the ideal class group of a CM-field goes to infinity with its absolute discriminant. This gives a positive answer to a question raised by Louboutin and Okazaki [4].

article

Number fields with the same index

Ilaria Corso, Roberto Dvornicich

Acta Arithmetica > 2002 > 102 > 4 > 323-337

article

On an equation in cyclotomic numbers

Roberto Dvornicich

Acta Arithmetica > 2001 > 98 > 1 > 71-94

article

Relations among Discriminant, Different, and Conductor of an Order

Ilaria Del Corso, Roberto Dvornicich

Journal of Algebra > 2000 > 224 > 1 > 77-90

article

A Lower Bound for the Height in Abelian Extensions

Francesco Amoroso, Roberto Dvornicich

Journal of Number Theory > 2000 > 80 > 2 > 260-272

We produce an absolute lower bound for the height of the algebraic numbers (different from zero and from the roots of unity) lying in an abelian extension of the rationals. The proof rests on elementary congruences in cyclotomic fields and on Kronecker–Weber theorem.

article

On Sums of Roots of Unity

Roberto Dvornicich, Umberto Zannier

Monatshefte für Mathematik > 2000 > 129 > 2 > 97-108

Abstract.Suppose that for some root of unity of order Q with and all coefficients ai belonging to a number field L. We bound Q in terms of k and . This generalizes a result of Conway and Jones for the case of rational coefficients. Moreover, we give an application to linear relations among characteristic functions of arithmetical progressions.

article

Uniformity over primes of tamely ramified splittings

Ilaria Del Corso, Roberto Dvornicich

manuscripta mathematica > 2000 > 101 > 2 > 239-266

Abstract:We fix a prime p and let f(X) vary over all monic integer polynomials of fixed degree n. Given any possible shape of a tamely ramified splitting of p in an extension of degree n, we prove that there exists a rational function (X)(X) such that the density of the monic integer polynomials f(X) for which the splitting of p has the given shape in [X]/f(X) is (p) (here reducible polynomials can...

article

On polynomials taking small values at integral arguments

Roberto Dvornicich, Umberto Zannier

Acta Arithmetica > 1982-1983 > 42 > 2 > 189-196

article

Linear independence of 'logarithms' in linear varieties

Roberto Dvornicich

Acta Arithmetica > 1980 > 36 > 4 > 407-417

Filter options

Publication date

Set your own date range

INFONA - science communication portal

Search results for: Roberto Dvornicich

Add recipient

Sending message cancelled

Are you sure you want to cancel sending this message?

Send message

Filter options

Publication date

Date range setting

Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.

Publication type

Keywords

Data set

Journal

Reporting an error / abuse

Sending the report failed

Accessibility options