An algorithmic construction of cyclic p-extensions of fields, with characteristic different from p, not containing the pth roots of unity
An Analogue of Artin-Schreier Theorem.
An analogue of Pfister's local-global principle in the burnside ring
Let be a Galois extension with Galois group . We study the set of -linear combinations of characters in the Burnside ring which give rise to -linear combinations of trace forms of subextensions of which are trivial in the Witt ring W of . In particular, we prove that the torsion subgroup of coincides with the kernel of the total signature homomorphism.
An application of Hilbert's irreducibility theorem to diophantine equations
An application of newton iteration procedure to -adic differential equations
An application of the Gelfand-Mazur theorem: the fundamental theorem of algebra revisited.
An Arithmetic Characterization of the Rational Homotopy Groups of Certain Spaces.
An arithmetic proof of Pop`s Theorem concerning Galois groups of function fields over number fields.
An efficient start system for multi-homogeneous polynomial continuation.
An elementary identity in the theory of Hecke L-functions.
An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors
Let L/K be a finite Galois extension of complete discrete valued fields of characteristic p. Assume that the induced residue field extension is separable. For an integer n ≥ 0, let denote the ring of Witt vectors of length n with coefficients in . We show that the proabelian group is zero. This is an equicharacteristic analogue of Hesselholt’s conjecture, which was proved before when the discrete valued fields are of mixed characteristic.
An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L p,k, and the finite field F(p k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L p,k) generated by L p,k into the variety V(F(p k)) generated by F(p k) and an interpretation Φ2 of V(F(p k)) into V(L p,k) such that Φ2Φ1(B) = B for every B ε V(L p,k) and Φ1Φ2(R) = R for every R ε V(F(p k)).
An example of a locally unbounded complete extension of the p-adic number field
An example of an arithmetic Fuchsian group.
An example of local analytic q-difference equation : Analytic classification
Using the techniques developed by Jean Ecalle for the study of nonlinear differential equations, we prove that the -difference equationwith () and is analytically conjugated to one of the following equations :
An existence theorem for systems of implicit differential equations
An explicit description of the set of all normal bases generators of a finite field
An explicit formula for the Mahler measure of a family of -variable polynomials
An explicit formula for the Mahler measure of the -variable Laurent polynomial is given, in terms of dilogarithms and trilogarithms.
An explicit integral polynomial whose splitting field has Galois group
Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group over typically have splitting field with Galois group isomorphic to the Weyl group of , we construct an explicit monic integral polynomial of degree whose splitting field has Galois group the Weyl group of the exceptional group of type .
An extension of approximation theorems