5 research outputs found
Generating series for irreducible polynomials over finite fields
We count the number of irreducible polynomials in several variables of a
given degree over a finite field. The results are expressed in terms of a
generating series, an exact formula and an asymptotic approximation. We also
consider the case of the multi-degree and the case of indecomposable
polynomials
Indecomposable polynomials and their spectrum
We address some questions concerning indecomposable polynomials and their
spectrum. How does the spectrum behave via reduction or specialization, or via
a more general ring morphism? Are the indecomposability properties equivalent
over a field and over its algebraic closure? How many polynomials are
decomposable over a finite field?Comment: 22 page