Submission date: 20 January 2017

Abstract:

I give a model-theoretic setting for the modular j function and its derivatives. These structures, here called j-fields, provide an adequate setting for interpreting the Ax-Schanuel theorem for j (Pila-Tsimerman 2015).
Following the ideas of M. Bays, J. Kirby and A.J. Wilkie for exponential fields, I prove a generic transcendence property for the j function.

Mathematics Subject Classification: 11J89, 03C60

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Full text arXiv 1701.05841: pdf, ps.