English

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}
}