Model Complete Expansions of the Real Field by Modular Functions and Forms
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2014
- DOI:
- 10.48550/arXiv.1406.7158
- arXiv:
- arXiv:1406.7158
- Bibcode:
- 2014arXiv1406.7158B
- Keywords:
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- Mathematics - Logic;
- 03C10 03C64 11F03 14H52 14K20 33E05
- E-Print:
- 14 pages, 1 figure