More calculations on determinant evaluations.
More on evaluating determinants
Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions
Let f be an arithmetic function and S = {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]) of x, and xj as its (i, j)-entry, respectively. The set S is said to be gcd closed if (xi, xj) ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj)) and (f[xi, xj]) if S consists of multiple coprime...
Multiplicative polynomials and Fermat's little theorem for non-primes.
Multiplicities of integer arrays.
Multiply integer-valued polynomials in a Galois field.
Multivariable polynomial injections on rational numbers
Near solutions of polynomial equations
Nested squares and evaluations of integer products.
Netted matrices.
New families of integer matrices whose leading principal minors form some well-known sequences.
Noether forms for the study of non-composite rational functions and their spectrum
Nombres de Pisots, matrices primitives et bêta-conjugués
Soit un nombre de Pisot ; nous montrons que pour tout entier assez grand il existe une matrice carrée à coefficients positifs ou nuls dont l’ordre est égal au degré de et dont est valeur propre.Soit le -développement de ; si est un nombre de Pisot, alors la suite est périodique après un certain rang (pour , ) et le polynômeest appelé polynôme de Parry. Nous montrons qu’il existe un ensemble relativement dense d’entiers tels que le polynôme minimal de est égal à son polynôme...
Nombres de racines d’un polynôme entier modulo
Nous montrons que l’ensemble des racines modulo une puissance d’un nombre premier d’un polynôme à coefficients entiers de degré est une union d’au plus progressions arithmétiques de modules assez grands. Nous en déduisons une majoration du nombre de ses racines dans un intervalle réel court.
Nonstandard arithmetic of iterated polynomials.
Normalität bezüglich Matrizen.
Norms in Quadratic Fields and Their Relations to Non Commuting 2x2 Matrices I.
Norms of factors of polynomials
Note on some greatest common divisor matrices
Some quadratic forms related to "greatest common divisor matrices" are represented in terms of L²-norms of rather simple functions. Our formula is especially useful when the size of the matrix grows, and we will study the asymptotic behaviour of the smallest and largest eigenvalues. Indeed, a sharp bound in terms of the zeta function is obtained. Our leading example is a hybrid between Hilbert's matrix and Smith's matrix.
Note sur la méthode d'élimination de Bezout