Ideal Matrices and Ideal Vectors.
Imbrications entre le théorème de Mason, la descente de Belyi et les différentes formes de la conjecture
Soient trois éléments de l’ensemble des entiers > (resp. ) des polynômes complexes) premiers entre eux ; on note le produit des facteurs premiers (resp. le nombre des facteurs premiers dans ) du produit . La conjecture énonce que, pour tout , il existe pour lequel l’inégalité : avec max) est toujours vérifiée. Le théorème de Mason établit l’inégalité, (supposé > ) désignant le plus grand des degrés des polynômes . Les cas de triplets de polynômes où l’égalité...
Indecomposable polynomials and their spectrum
Inequalities on polynomial heights.
Inequalities related to rearrangements of powers and symmetric polynomials.
Infinite divisibility of Smith matrices
Integer matrices related to Liouville's function
In this note, we construct some integer matrices with determinant equal to certain summation form of Liouville's function. Hence, it offers a possible alternative way to explore the Prime Number Theorem by means of inequalities related to matrices, provided a better estimate on the relation between the determinant of a matrix and other information such as its eigenvalues is known. Besides, we also provide some comparisons on the estimate of the lower bound of the smallest singular value. Such discussion...
Integer-valued polynomials on algebras: a survey
We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature.
Inversion of generating functions using determinants.
Irreducible polynomials with many roots of equal modulus
Iterations of concave maps, the Perron-Frobenius theory, and applications to circle packings.