NUMBER OF IRREDUCIBLE POLYNOMIALS IN SEVERAL VARIABLES OVER FINITE FIELDS

As in the ergodic theoretical proof of Szemer´edi’s theorem (as well as its extension to polynomial progressions), the analogy between sets of integers with positive upper

In this note, we find the asymptotic main term of the variance of the number of roots of Kostlan–Shub–Smale random polynomials and prove a central limit theorem for this number of

Extreme points determine a fundamental subset of the cone: by Carath´eodory’s Theorem (see Theorem 2.2), if the dimension of the vector space is finite and under some

The structure of the paper is the following: in Sections 2 and 3 we collect preliminary results, in Section 4 we prove the results concerning Kummer degrees related to powers of a

Recall from [1, Theorem 14] that a good basis of G always exists, and from [1, Section 6.1] that a good basis and the parameters for the divisibility are computable.

Some of these bounds turn out to be asymptotically optimal when g → ∞ , meaning that they converge to the lower bound from the generalized Brauer–Siegel theorem for function

The isogeny class of an abelian variety over a finite field is determined by its characteristic polynomial (i.e. the characteristic polynomial of its Frobenius en- domorphism)..

Since the charac- teristic polynomial of a non-simple abelian variety is a product of characteristic polynomials of abelian varieties of smaller dimensions and our problem is