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Mathieu equation and Elliptic curve

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arxiv 1006.5185 v3 pith:3M6O33MZ submitted 2010-06-27 math-ph hep-thmath.MP

Wei He , Yan-Gang Miao This is my paper
classification math-phhep-thmath.MP
keywords curveellipticequationmathieudifferentialorderalongcertain
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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 $q<<1$ and $q>>1$, 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.

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  1. Regular and Floquet bases for gauge and gravity theories: a non perturbative approach

    hep-th 2025-08 conditional novelty 7.0 of 10

    A new kink method computes the Floquet phase of Heun-type equations as convergent series, matching the dual gauge period of N=2 SYM in the NS background and giving black-hole perturbation wavefunctions.

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