Automorphic forms for triangle groups
Number Theory
2013-07-17 v1 High Energy Physics - Theory
Group Theory
Abstract
For triangle groups, the (quasi-)automorphic forms are known just as explicitly as for the modular group SL. We collect these expressions here, and then interpret them using the Halphen differential equation. We study the arithmetic properties of their Fourier coefficients at cusps and Taylor coefficients at elliptic fixed-points --- in both cases integrality is related to the arithmeticity of the triangle group. As an application of our formulas, we provide an explicit modular interpretation of periods of 14 families of Calabi-Yau threefolds over the thrice-punctured sphere.
Cite
@article{arxiv.1307.4372,
title = {Automorphic forms for triangle groups},
author = {Charles F. Doran and Terry Gannon and Hossein Movasati and Khosro Monsef Shokri},
journal= {arXiv preprint arXiv:1307.4372},
year = {2013}
}
Comments
32 pages