EuDML | Browse

The paper consists of two parts, both related to problems of Lubelski, but unrelated otherwise. Theorem 1 enumerates for a = 1,2 the finitely many positive integers D such that every odd positive integer L that divides x² +Dy² for (x,y) = 1 has the property that either L or $2^{a} L$ is properly represented by x²+Dy². Theorem 2 asserts the following property of finite extensions k of ℚ : if a polynomial f ∈ k[x] for almost all prime ideals of k has modulo at least v linear factors, counting multiplicities,...

Some classes of irreducible polynomials

Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat (2006)

Acta Arithmetica

Some quartic number fields containing an imaginary quadratic subfield

Stéphane R. Louboutin (2011)

Colloquium Mathematicae

Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.

Specializations of one-parameter families of polynomials

Farshid Hajir, Siman Wong (2006)

Annales de l’institut Fourier

Let $K$ be a number field, and suppose $λ (x, t) \in K [x, t]$ is irreducible over $K (t)$ . Using algebraic geometry and group theory, we describe conditions under which the $K$ -exceptional set of $λ$ , i.e. the set of $α \in K$ for which the specialized polynomial $λ (x, α)$ is $K$ -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed $n \geq 10$ , all but finitely many $K$ -specializations of the degree $n$ generalized Laguerre polynomial $L_{n}^{(t)} (x)$ are $K$ -irreducible and have Galois group $S_{n}$ . Second, we study specializations...

Stabilité algébrique et topologies hilbertiennes

Pierre Liardet (1975/1976)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Suites récurrentes et polynômes à plusieurs variables

Jean-Paul Bezivin (1982/1983)

Groupe de travail d'analyse ultramétrique

Sur les polynômes à coefficients entiérs et de discriminant donné

Kalman Győry (1973)

Acta Arithmetica

The Approximation of Solutions to Linear Homogeneous Differential Equations by Rational Functions.

Charles Osgood (1980)

Monatshefte für Mathematik

The EM Algorithm applied to determining new limit points of Mahler measures

Souad El Otmani, Georges Rhin, Jean-Marc Sac-Épée (2010)

Control and Cybernetics

The factorization of certain quadrinominals.

W.H. Mills (1985)

Mathematica Scandinavica

The integer transfinite diameter of intervals and totally real algebraic integers

V. Flammang, G. Rhin, C. J. Smyth (1997)

Journal de théorie des nombres de Bordeaux

In this paper we build on some recent work of Amoroso, and Borwein and Erdélyi to derive upper and lower estimates for the integer transfinite diameter of small intervals $[\frac{r}{s}, \frac{r}{s} + δ]$ , where $\frac{r}{s}$ is a fixed rational and $δ \to 0$ . We also study functions $g_{-}, g, g^{+}$ associated with transfinite diameters of Farey intervals. Then we consider certain polynomials, which we call critical polynomials, associated to a given interval $I$ . We show how to estimate from below the proportion of roots of an integer polynomial which is sufficiently...

The Lehmer constants of an annulus

Artūras Dubickas, Chris J. Smyth (2001)

Journal de théorie des nombres de Bordeaux

Let $M (α)$ be the Mahler measure of an algebraic number $α$ , and $V$ be an open subset of $ℂ$ . Then its Lehmer constant $L (V)$ is inf $M {(α)}^{1 / deg (α)}$ , the infimum being over all non-zero non-cyclotomic $α$ lying with its conjugates outside $V$ . We evaluate $L (V)$ when $V$ is any annulus centered at $0$ . We do the same for a variant of $L (V)$ , which we call the transfinite Lehmer constant $L_{\infty} (V)$ .Also, we prove the converse to Langevin’s Theorem, which states that $L (V) > 1$ if $V$ contains a point of modulus $1$ . We prove the corresponding result for $L_{\infty} (V)$ .

Currently displaying 161 – 180 of 199

Previous Page 9 Next

Displaying 161 – 180 of 199

Résultats de stabilité algébrique.

Schinzel's conjecture H and divisibility in abelian linear recurring sequences

Sequences of reducible ${0, 1}$ -polynomials modulo a prime.

Small limit points of Mahler's measure.

Solution to a Problem of Lubelski and an Improvement of a Theorem of His