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Mean field equations, hyperelliptic curves and modular forms: I

Ching-Li Chai U. Pennsylvania Chang-Shou Lin National Taiwan U. Chin-Lung Wang National Taiwan U.

Analysis of PDEs mathscidoc:1610.03001

Cambridge J. Math., 3, 127-274, 2015
We develop a theory to connect the following three areas: (a) the mean field equations on flat tori, (b) the classical Lame equations and (c) modular forms. A major theme in part I is a classification of developing maps f attached to solutions of the mean field equation according to the types of transformation laws (or monodromy) with respect to the period lattice satisfied by f.
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@inproceedings{ching-li2015mean,
  title={Mean field equations, hyperelliptic curves and modular forms: I},
  author={Ching-Li Chai, Chang-Shou Lin, and Chin-Lung Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161003233327137092077},
  booktitle={Cambridge J. Math.},
  volume={3},
  pages={127-274},
  year={2015},
}
Ching-Li Chai, Chang-Shou Lin, and Chin-Lung Wang. Mean field equations, hyperelliptic curves and modular forms: I. 2015. Vol. 3. In Cambridge J. Math.. pp.127-274. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161003233327137092077.
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