Mathieu equation and Elliptic curve
Mathematical Physics
2015-05-19 v3 High Energy Physics - Theory
math.MP
Abstract
We present a relation between the Mathieu equation and a particular elliptic curve. We find that the Floquet exponent of the Mathieu equation, for both and , can be obtained from the integral of a differential one form along the two homology cycles of the elliptic curve. Certain higher order differential operators are needed to generate the WKB expansion. We provide a fifth order proof.
Cite
@article{arxiv.1006.5185,
title = {Mathieu equation and Elliptic curve},
author = {Wei He and Yan-Gang Miao},
journal= {arXiv preprint arXiv:1006.5185},
year = {2015}
}
Comments
12 pages; minor improvement of the Conclusion section, references added