Abstract
In analogy with algebraic equations with S-units, we shall deal with S-unit points in an analytic hypersurface, or more generally with values of analytic functions at S-unit points. After proving a general theorem, we shall give diophantine applications to certain problems of integral points on subvarieties of A 1 × G m n . Also, we shall prove an analogue of a theorem of Masser, important in Mahler's method for transcendence. In the course of the proofs we shall also develop a theory for those algebraic subgroups of G m n whose Zariski closure in A n contains the origin. Among others, we shall prove a structure theorem for the family of such subgroups contained in a given analytic hypersurface, obtaining conclusions similar to the case of algebraic varieties.
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