A remark on the Chebotarev theorem about roots of unity.
A stability analysis for finite volume schemes applied to the Maxwell system
We present in this paper a stability study concerning finite volume schemes applied to the two-dimensional Maxwell system, using rectangular or triangular meshes. A stability condition is proved for the first-order upwind scheme on a rectangular mesh. Stability comparisons between the Yee scheme and the finite volume formulation are proposed. We also compare the stability domains obtained when considering the Maxwell system and the convection equation.
A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function
We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli relations,...
A way of Reducing the Factorization Problem in Z[x] to the Factorization Problem in Z
Abschätzungen ganzzahliger Polynome auf dem Intervall [0, 1].
Addendum to the paper: "On the number of terms of a composite polynomial" (Acta Arith. 127 (2007), 157-167)
Addendum to the papers "On polynomials taking small values at integral arguments I, II" (Acta Arith. 42 (1983), 189-196; ibid. 106 (2003), 115-121)
Advanced determinant calculus.
An Arithmetic Characterization of the Rational Homotopy Groups of Certain Spaces.
An effective procedure for minimal bases of ideals in Z[x]
We give an effective procedure to find minimal bases for ideals of the ring of polynomials over the integers.
An Egyptian algorithm for polynomials.
An explicit formula for the Mahler measure of a family of -variable polynomials
An explicit formula for the Mahler measure of the -variable Laurent polynomial is given, in terms of dilogarithms and trilogarithms.
An extension of a result of C. J. Smyth to polynomials in several variables
An irreducibility criterion for composition of polynomials.
An irreducibility criterion for polynomials in several variables
An upper bound for the norm of a gcd-related matrix.
Anneaux de Fatou
Approximate polynomial GCD
The computation of polynomial greatest common divisor (GCD) ranks among basic algebraic problems with many applications, for example, in image processing and control theory. The problem of the GCD computing of two exact polynomials is well defined and can be solved symbolically, for example, by the oldest and commonly used Euclid’s algorithm. However, this is an ill-posed problem, particularly when some unknown noise is applied to the polynomial coefficients. Hence, new methods for the GCD computation...
Approximation d'un nombre p-adique par des nombres algebriques
Asymptotic distribution and symmetric means of algebraic numbers
Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the problem that include questions on the smallest limit points of symmetric means. The key tool used in the study is the asymptotic distribution of algebraic numbers understood via the weak* limits of their counting measures. We establish interesting properties of the...