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Open Access

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

Contributed equally
Research in Number Theory20151:4

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.


Partition FunctionModular FormModular FunctionMaass FormHolomorphic Modular Form