@article{b9d1dfdef70246a6b3b0d01347dabfb5,
title = "The Hauptmodul at elliptic points of certain arithmetic groups",
abstract = "Let $N$ be a square-free integer such that the arithmetic group $\Gamma_0(N)^+$ has genus zero; there are $44$ such groups. Let $j_N$ denote the associated Hauptmodul normalized to have residue equal to one and constant term equal to zero in its $q$-expansion. In this article we prove that the Hauptmodul at any elliptic point of the surface associated to $\Gamma_0(N)^+$ is an algebraic integer. Moreover, for each such $N$ and elliptic point $e$, we show how to explicitly evaluate $j_{N}(e)$. Furthermore, we provide a list of generating polynomials (with small cefficients) of the class fields of the orders over the imaginary quadratic extension of rationals corresponding to the elliptic points under consideration.",
keywords = "Hauptmoduli, Class fields, Singular moduli",
author = "Jay Jorgenson and Lejla Smajlovi{\'c} and H. Then",
year = "2019",
month = apr,
day = "17",
doi = "10.1016/j.jnt.2019.03.021",
language = "English",
journal = "International Journal of Number Theory",
issn = "1793-0421",
publisher = "World Scientific Publishing Co.",
}