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

被引：1
|
作者：
Mertens M.H. [1 ]
Rolen L. [1 ]
机构：
[1] Mathematisches Institut der Universität zu Köln, Weyertal 86-90, Köln
来源：
Research in Number Theory | / 1卷 / 1期
基金：
欧洲研究理事会;
关键词：
Partition Function; Modular Form; Modular Function; Maass Form; Holomorphic Modular Form;
D O I：
10.1007/s40993-015-0007-5
中图分类号：
学科分类号：
摘要：
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. © 2015, Martens and Rolen.; licensee Springer.
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