On a galoisian approach to the splitting of separatrices
On a general difference Galois theory I
We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic , we attach its Galois group, which is a group of coordinate transformation.
On a general difference Galois theory II
We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.
On Apery's differential operator
On Certain Properties of Soloutions of Second-Order Linear Differential Equations.
On differential independence of the Riemann zeta function and the Euler gamma function
On differential rational invariants of finite subgroups of affine group.
On exponents of p-adic differential modules.
On th order differential equations over Hardy fields
On ordinary linear -adic differential equations with algebraic function coefficients
On overconvergent isocrystals and -isocrystals of rank one
On p-adic monodromy.
On rings of constants of derivations in two variables in positive characteristic
Let k be a field of chracteristic p > 0. We describe all derivations of the polynomial algebra k[x,y], homogeneous with respect to a given weight vector, in particular all monomial derivations, with the ring of constants of the form , where .
On Second Order Linear Differential Equations with Few Transcendental Solutions.
On the bialgebra of functional graphs and differential algebras.
On the calculation of some differential galois groups.
On the Galois theory of difference fields.
On the geometrization of a lemma of Singer and van der Put
In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory, used by Singer and van der Put in their reference book. This geometrization, in addition of giving a nice insight on this result, offers us the opportunity to investigate several points of differential algebra and differential algebraic geometry. We study the class of simple Δ-schemes and prove that they all have a coarse space of leaves. Furthermore, instead of considering schemes endowed with...
On the index theorem for -adic differential equations. III. (Sur le théorème de l'indice des équations différentielles -adiques. III.)
On the -adic continuation of the logarithmic derivative of certain hypergeometric functions