On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono
Number Theory
2020-07-02 v4
Abstract
Recently, Bruinier and Ono found an algebraic formula for the partition function in terms of traces of singular moduli of a certain non-holomorphic modular function. In this paper we prove that the rational polynomial having these singuar moduli as zeros is (essentially) irreducible, settling a question of Bruinier and Ono. The proof uses careful analytic estimates together with some related work of Dewar and Murty, as well as extensive numerical calculations of Sutherland.
Keywords
Cite
@article{arxiv.1501.03743,
title = {On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono},
author = {Michael H. Mertens and Larry Rolen},
journal= {arXiv preprint arXiv:1501.03743},
year = {2020}
}