On the congruence , where q is a prime and f is a k-normal polynomial
On the density of some sets of primes connected with cyclotomic polynomials
On the enumeration of quintic fields with small discriminant.
On the Galois groups of cubics and trinomials
On the Győry-Sárközy-Stewart conjecture in function fields
We consider function field analogues of the conjecture of Győry, Sárközy and Stewart (1996) on the greatest prime divisor of the product for distinct positive integers , and . In particular, we show that, under some natural conditions on rational functions , the number of distinct zeros and poles of the shifted products and grows linearly with if . We also obtain a version of this result for rational functions over a finite field.
On the height of algebraic numbers with real conjugates
On the irreducibility of 0,1-polynomials of the form f(x)xⁿ + g(x)
If f(x) and g(x) are relatively prime polynomials in ℤ[x] satisfying certain conditions arising from a theorem of Capelli and if n is an integer > N for some sufficiently large N, then the non-reciprocal part of f(x)xⁿ + g(x) is either identically ±1 or is irreducible over the rationals. This result follows from work of Schinzel in 1965. We show here that under the conditions that f(x) and g(x) are relatively prime 0,1-polynomials (so each coefficient is either 0 or 1) and f(0) = g(0) = 1, one...
On the irreducibility of -quadrinomials.
On the irreducibility of a class of polynomials, IV
On the irreducibility of neighbouring polynomials
On the irreducibility of the generalized Laguerre polynomials
On the irreducible factors of a polynomial over a valued field
We explicitly provide numbers , such that each irreducible factor of a polynomial with integer coefficients has a degree greater than or equal to and can have at most irreducible factors over the field of rational numbers. Moreover, we prove our result in a more general setup for polynomials with coefficients from the valuation ring of an arbitrary valued field.
On the Lehmer constant of finite cyclic groups
On the Mahler measure of the composition of two polynomials
On the number of irreducible factors of a polynomial II
On the number of polynomials of bounded measure
On the product of heights of algebraic numbers summing to real numbers
On the product of the conjugates outside the unit circle of an algebraic number
On the reducibility type of trinomials
On the relation between two conjectures on polynomials