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

Mertens, Michael H and Rolen, Larry (2015) On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono. Research in Number Theory, 1 (1). 4-.

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Official URL: http://dx.doi.org/10.1007/s40993-015-0007-5

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.

Item Type:	Article
Uncontrolled Keywords:	math.NT, math.NT
Depositing User:	Symplectic Admin
Date Deposited:	01 Jul 2020 08:50
Last Modified:	18 Jan 2023 23:47
DOI:	10.1007/s40993-015-0007-5
Open Access URL:	https://link.springer.com/article/10.1007/s40993-0...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3092357