Model Complete Expansions of the Real Field by Modular Functions and Forms

Ricardo Bianconi

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arXiv · 1406.7158

Model Complete Expansions of the Real Field by Modular Functions and Forms

Ricardo Bianconi

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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 \cite{peterzil-starchenko-wp2004} on the uniform definability of $\wp$ function in $\mathbb{R}_{\mathit{an}}$ (and of the modular function $J$). In the conclusion we pose some open problems related to this work.

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Ricardo Bianconi. 2014-06-27. Model Complete Expansions of the Real Field by Modular Functions and Forms. https://arxiv.org/abs/1406.7158

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