Analytic Continuation of Currents and Division Problems.
Un algorithme est présenté pour calculer en toute généralité le « réseau de Levelt » pour un réseau donné.
We generalize and unify the proofs of several results on algebraic independence of arithmetic functions and Dirichlet series by using a theorem of Ax on the differential Schanuel conjecture. Along the way, we find counter-examples to some results in the literature.
We survey recent work on arithmetic analogues of ordinary and partial differential equations.