On canonical subfield preserving polynomials
Explicit monoid structure is provided for the class of canonical subfield preserving polynomials over finite fields. Some classical results and asymptotic estimates will follow as corollaries.
On certain algebraic curves related to polynomial maps
On Certain Properties of Soloutions of Second-Order Linear Differential Equations.
On chains of purely transcendental field extensions
On characterizing nearfields.
On Chinburg's second conjecture for abelian fields.
On Commutative Semigroups of Polynomials with Respect to Composition.
On completeness of left-invariant Lorentz metrics on solvable Lie groups.
We study geodesic completeness for left-invariant Lorentz metrics on solvable Lie groups.
On congruence topologies in number fields.
On convergence of Börsch-Supan's method with Weierstrass' corrections.
On convergence of integrals in o-minimal structures on archimedean real closed fields
We define a notion of volume for sets definable in an o-minimal structure on an archimedean real closed field. We show that given a parametric family of continuous functions on the positive cone of an archimedean real closed field definable in an o-minimal structure, the set of parameters where the integral of the function converges is definable in the same structure.
On convex topological halfalgebras
On cubic factors of certain trinominals.
On degrees of three algebraic numbers with zero sum or unit product
Let α, β and γ be algebraic numbers of respective degrees a, b and c over ℚ such that α + β + γ = 0. We prove that there exist algebraic numbers α₁, β₁ and γ₁ of the same respective degrees a, b and c over ℚ such that α₁ β₁ γ₁ = 1. This proves a previously formulated conjecture. We also investigate the problem of describing the set of triplets (a,b,c) ∈ ℕ³ for which there exist finite field extensions K/k and L/k (of a fixed field k) of degrees a and b, respectively, such that the degree of the...
On differential independence of the Riemann zeta function and the Euler gamma function
On differential rational invariants of finite subgroups of affine group.
On dihedral algebraic function fields
On double covers of the generalized alternating group as Galois groups over algebraic number fields
Let mℤd ≀ mℤd ≀ mℤd ≀ m
On duality over a certain divided power algebra with positive characteristic.
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...