We will develop the machinery of resultants and resolvent polynomials with the ultimate goal of understanding the so-called “resolvent method” for computing Galois groups over Q. Along the way, we will encounter tangential applications of these tools, such as the determination of the minimal polynomial of, say, the sum of two algebraic numbers using resultants. In this way, this paper can serve...

This article considers the n-number Ducci game as a linear map over the n dimensional vector space ZZn 2 . Period lengths are characterized as orders of factors of the minimal polynomial of that transformation. The minimal polynomial can be explicitly obtained for any n. We provide algebraic proofs of divisibility conditions, initially found by Ehrlich. In addition, all periodic cycle lengths f...

Let E be an elliptic curve defined over Q. The aim of this paper is to make it possible to compute Heegner L-functions and anticyclotomic Λ-adic regulators of E, which were studied by Mazur-Rubin and Howard. We generalize results of Cohen and Watkins, which enable us to compute Heegner points of non-fundamental discriminant. We then prove a relationship between the denominator of a point of E d...

We consider the sequences over the finite field of four elements obtained by inverse Gray mapping from a pair of binary sequences. We derive the linear complexity and the minimal polynomial of sequences constructed from Legendre sequences, Hall’s sextic sequences and twin-prime sequences using the technique proposed by Tang, Ding, Lim, Kim et al.

We study real algebraic plane curves, at an elementary level, using as little algebra as possible. Both cases, affine and projective, are addressed. A real curve is infinite, finite or empty according to the fact that a minimal polynomial for the curve is indefinite, semi–definite nondefinite or definite. We present a discussion about isolated points. By means of the operator, these points can ...

In this work we devise three classes of recursion relations that can be used for implementing some extrapolation methods for vector sequences. One class of recursion relations can be used to implement methods like the modified minimai polynomial extrapolation and the topological epsilon algorithm, another allows implementation of methods like minimal polynomial and reduced rank extrapolation, w...

We construct a generator system of the annihilator of a generalized Verma module of a reductive Lie algebra induced from a character of a parabolic subalgebra as an analogue of the minimal polynomial of a matrix.

The coefficients and the discriminant of the octic period polynomial i/^z) are computed, where, for a prime p = 8/ + 1, ^(r) denotes the minimal polynomial over Q of the period (1/%)2.%Z¡ exp(2trins/p). Also, the finite set of prime octic nonresidues (mod p) which divide integers represented by i|/8(z) is characterized.

We construct a generator system of the annihilator of a generalized Verma module of a classical reductive Lie algebra induced from a character of a parabolic subalgebra as an analogue of the minimal polynomial of a matrix. In a classical limit it gives a generator system of the defining ideal of any semisimple co-adjoint orbit of the Lie algebra. We also give some applications to integral geome...