EuDML | Browse

Items

All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 19 of 19

Schinzel's problem: Imprimitive covers and the monodromy method

Michael D. Fried, Ivica Gusić (2012)

Acta Arithmetica

Sharper ABC-based bounds for congruent polynomials

Daniel J. Bernstein (2005)

Journal de Théorie des Nombres de Bordeaux

Agrawal, Kayal, and Saxena recently introduced a new method of proving that an integer is prime. The speed of the Agrawal-Kayal-Saxena method depends on proven lower bounds for the size of the multiplicative semigroup generated by several polynomials modulo another polynomial $h$ . Voloch pointed out an application of the Stothers-Mason ABC theorem in this context: under mild assumptions, distinct polynomials $A, B, C$ of degree at most $1.2 deg h - 0.2 deg rad A B C$ cannot all be congruent modulo $h$ . This paper presents two improvements...

Simples remarques sur les racines entières des équations cubiques

S. Realis (1875)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Simples remarques sur les racines entières des équations cubiques

S. Realis (1875)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros

James McKee, Chris Smyth (2013)

Open Mathematics

We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class, the cyclogenic...

Singular differences of powers of $2 \times 2$ -matrices

J.-H. Evertse, R. Tijdeman (1996)

Compositio Mathematica

Small limit points of Mahler's measure.

Boyd, David W., Mossinghoff, Michael J. (2005)

Experimental Mathematics

Some classes of irreducible polynomials

Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat (2006)

Acta Arithmetica

Sommes de carrés de polynômes irréductibles dans $F_{q} [X]$

Mireille Car (1984)

Acta Arithmetica

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...