Abstract
Abstract : Work focused on the study of analytic, arithmetic and algorithmic properties of differential equations applied to solutions of problems in theoretical mathematics, mathematical and theoretical physics, numerical methods and computer science. Work in the area of effective approximation methods in diophantine geometry, differential equations and computer realizations have progressed in several directions. In diophantine approximations the relationship is studied between complex-analytic and arithmetic (p-adic) properties of linear differential equations using Pade approximations methods. Another part of our work is aimed at complete determination of all (linear) differential equations having arithmetic sense. In many cases it is shown that all these equations arise from Geometry (are variations of period structures of algebraic manifolds) . This work of ours is closely connected with the study of the arithmetic properties of classical constants of analysis. The common analytic method in all these studies is the method of Pade approximations to solutions to special linear differential equations.
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