Equations D3 and spectral elliptic curves
Number Theory
2016-09-20 v1
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.
Cite
@article{arxiv.1212.0205,
title = {Equations D3 and spectral elliptic curves},
author = {Vasily Golyshev and Masha Vlasenko},
journal= {arXiv preprint arXiv:1212.0205},
year = {2016}
}