Ax-Schanuel for the j-function
classification
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math.NT
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j-functionax-schanuelrelationsalgebraicanalogueassertsatypicalcompositions
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In this paper we prove a functional transcendence statement for the j-function which is an analogue of the Ax-Schanuel theorem for the exponential function. It asserts, roughly, that atypical algebraic relations among functions and their compositions with the j-function are governed by modular relations.
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