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.

Access the full-text of this item by clicking on the Open Access link.

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: 09 Jan 2021 01:58
DOI: 10.1007/s40993-015-0007-5
Open Access URL: https://link.springer.com/article/10.1007/s40993-0...
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3092357