The constants of the Volterra derivation
The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.
The differential equation y' = fy in the algebras H(D).
The differential Galois theory of regular singular p-adic differential equations.
The differential spectrum of a ring
The equation in when is quasi-invertible
The five-variable Volterra system
We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.
The fourteenth problem of Hilbert for polynomial derivations
We present some facts, observations and remarks concerning the problem of finiteness of the rings of constants for derivations of polynomial rings over a commutative ring k containing the field ℚ of rational numbers.
The Global Homological Dimension of Some Algebras of Differential Operators.
The Lamé family of connections on the projective line
This paper deals with rank two connections on the projective line having four simple poles with prescribed local exponents 1/4 and . This Lamé family of connections has been extensively studied in the literature. The differential Galois group of a Lamé connection is never maximal : it is either dihedral (finite or infinite) or reducible. We provide an explicit moduli space of those connections having a free underlying vector bundle and compute the algebraic locus of those reducible connections....
The -adic local monodromy theorem for fake annuli
The p-adic differential equation y' = wy in the closed unit disk.
The Picard-Vessiot closure in differential Galois theory
The Set of Derivatives in a Non-Archimedean Field.
The structure of strongly normal difference extensions.
Théorèmes de division sur et applications
Théories cohomologiques.
Théories de Galois différentielles et transcendance
On décrit des preuves galoisiennes des versions logarithmique et exponentielle de la conjecture de Schanuel, pour les variétés abéliennes sur un corps de fonctions.
Travaux récents de Ju. V. Nesterenko
Travaux récents sur les points singuliers des équations différentielles linéaires
Two remarks about Picard-Vessiot extensions and elementary functions
We present a simple proof of the theorem which says that for a series of extensions of differential fields K ⊂ L ⊂ M, where K ⊂ M is Picard-Vessiot, the extension K ⊂ L is Picard-Vessiot iff the differential Galois group is a normal subgroup of . We also present a proof that the probability function Erf(x) is not an elementary function.