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  • Research Article
  • Open Access

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

Contributed equally
Research in Number Theory20151:4

https://doi.org/10.1007/s40993-015-0007-5

  • Received: 17 January 2015
  • Accepted: 3 February 2015
  • Published:

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 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.

Keywords

  • Partition Function
  • Modular Form
  • Modular Function
  • Maass Form
  • Holomorphic Modular Form

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