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Logarithmic Newton polygons and polytopes, and the factorization of Dirichlet polynomials
Nicolae Ciprian Bonciocat
To study a Dirichlet polynomial by regarding it as a multivariate polynomial via the canonical map sending to…
Some factorization results for bivariate polynomials
Nicolae Ciprian Bonciocat, Rishu Garg, Jitender Singh
We provide upper bounds on the total number of irreducible factors, and in particular irreducibility criteria for some classes of bivariate polynomials over an arbitrary f…
Irreducibility criteria for pairs of polynomials whose resultant is a prime number
Nicolae Ciprian Bonciocat
We obtain various irreducibility criteria for pairs of polynomials with integer coefficients whose resultant is a prime number, or is divisible by a suffic…
Apollonius circles and the number of irreducible factors of polynomials
Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat, Yann Bugeaud +2
We provide upper bounds for the sum of the multiplicities of the non-constant irreducible factors that appear in the canonical decomposition of a polynomial ,…
Zero-free angular sectors and lens-shaped regions for polynomials, with applications to irreducibility
Ciprian Mircea Bonciocat, Nicolae Ciprian Bonciocat
For a real polynomial we present explicit zero-free angular sectors in the complex plane, symmetric with respect to the real axis, with angles depending only on the degree of $…
Apollonius circles and irreducibility criteria for polynomials
Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat, Yann Bugeaud +1
We prove the irreducibility of integer polynomials whose roots lie inside an Apollonius circle associated to two points on the real axis with integer abscisae and , w…
Schönemann-Eisenstein-Dumas-type irreducibility conditions that use arbitrarily many prime numbers
Nicolae Ciprian Bonciocat
The famous irreducibility criteria of Schönemann-Eisenstein and Dumas rely on information on the divisibility of the coefficients of a polynomial by a single prime number. In this…