On the zeta function of monodromy of a polynomial map
In this paper we consider the prehomogeneous vector space for a pair of simple algebras which are inner forms of the type and the type. We mainly study the non-split cases. The main purpose of this paper is to determine the principal parts of the global zeta functions associated with these spaces when the simple algebras are non-split. We also give a description of the sets of rational orbits of these spaces, which clarifies the expected density theorems arising from the properties of these...
We answer three reducibility (or irreducibility) questions for -polynomials, those polynomials which have every coefficient either or . The first concerns whether a naturally occurring sequence of reducible polynomials is finite. The second is whether every nonempty finite subset of an infinite set of positive integers can be the set of positive exponents of a reducible -polynomial. The third is the analogous question for exponents of irreducible -polynomials.