Submission date: 27 June 2014.

Abstract:

We prove a strong form of model completenes for expansions of the field of real numbers by (the real and imaginary parts of) the modular function J, by the modular forms E_4 and E_6 and quasimodular form E_2 defined in the usual fundamental domain, and the restricted sine function and the (unrestricted) exponential function. This is done using ideas of Peterzil and Starchenko's paper on the uniform definability of \wp function in R_{an} (and of the modular function J). In the conclusion we pose some open problems related to this work.

Mathematics Subject Classification: 3C10 03C64 11F03 14H52 14K20 33E05

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Full text arXiv 1406.7158: pdf, ps.