On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono
© Martens and Rolen.; licensee Springer. 2015
Received: 17 January 2015
Accepted: 3 February 2015
Published: 30 November 2015
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 singular 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.