On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono

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.

References in corpus (1)

• Class polynomials for nonholomorphic modular functions

Cited by in corpus (2)

• A Modular Andre-Oort Statement with Derivatives
• Class invariants for certain non-holomorphic modular functions