Universität zu Köln

Griffin, Michael and Rolen, Larry (2015). Integrality properties of class polynomials for non-holomorphic modular functions. J. Ramanujan Math. Soc., 30 (1). S. 83 - 100. MYSORE: RAMANUJAN MATHEMATICAL SOC. ISSN 2320-3110

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Abstract

In his paper Traces of Singular Moduli [14], Zagier studied values of certain modular functions at imaginary quadratic points known as singular moduli. He proved that traces of these algebraic integers are Fourier coefficients of certain half-integral weight modular forms. In this paper, he obtained similar results for certain non-holomorphic modular functions. However, he observed that these singular moduli are not necessarily algebraic integers. Based on numerical examples, the class polynomials whose roots are these singular moduli seem to have predictable denominators. Here we explain this phenomenon and provide a sharp bound on these denominators.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Griffin, Michael UNSPECIFIED UNSPECIFIED UNSPECIFIED Rolen, Larry UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-405963
Journal or Publication Title:	J. Ramanujan Math. Soc.
Volume:	30
Number:	1
Page Range:	S. 83 - 100
Date:	2015
Publisher:	RAMANUJAN MATHEMATICAL SOC
Place of Publication:	MYSORE
ISSN:	2320-3110
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language FORMS; VALUES; WEIGHT Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/40596