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arXiv · 1212.0205

Equations D3 and spectral elliptic curves

Vasily Golyshev·Masha Vlasenko
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Abstract

We study modular determinantal differential equations of orders 2 and 3. We show that the expansion of the analytic solution of a non-degenerate modular equation of type D3 over the rational numbers with respect to the natural parameter coincides, under certain assumptions, with the q-expansion of the newform of its spectral elliptic curve and therefore possesses a multiplicativity property. We compute the complete list of D3 equations with this multiplicativity property and relate it to Zagier's list of non-degenerate modular D2 equations.

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Vasily Golyshev, Masha Vlasenko. 2012-12-02. Equations D3 and spectral elliptic curves. https://arxiv.org/abs/1212.0205

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