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arXiv · 1501.03743

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

Michael H. Mertens·Larry Rolen
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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.

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Michael H. Mertens, Larry Rolen. 2015-08-24. On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono. https://doi.org/10.1007/s40993-015-0007-5

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