Singular moduli for a distinguished non-holomorphic modular function

Authors:
Valerio Dose, Nathan Green, Michael Griffin, Tianyi Mao, Larry Rolen and John Willis

Journal:
Proc. Amer. Math. Soc. **143** (2015), 965-972

MSC (2010):
Primary 11F12, 11G15

Published electronically:
October 29, 2014

MathSciNet review:
3293714

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Abstract | References | Similar Articles | Additional Information

Abstract: Here we study the integrality properties of singular moduli of a special non-holomorphic function , which was previously studied by Siegel, Masser, and Bruinier, Sutherland, and Ono. Similar to the modular -invariant, has algebraic values at any CM-point. We show that primes dividing the denominators of these values must have absolute value less than that of the discriminant and are not split in the corresponding quadratic field. Moreover, we give a bound for the size of the denominator.

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Additional Information

**Valerio Dose**

Affiliation:
Department of Mathematics, University of Rome Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy

Email:
dose@mat.uniroma2.it

**Nathan Green**

Affiliation:
Department of Mathematics, 275 TMCB Brigham Young University, Provo, Utah 84602

Email:
jaicouru@gmail.com

**Michael Griffin**

Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322

Email:
mjgrif3@emory.edu

**Tianyi Mao**

Affiliation:
The Graduate Center, City University of New York, 365 Fifth Avenue, Room 4208, New York, New York 10016

Email:
tmao@gc.cuny.edu

**Larry Rolen**

Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322

Email:
lrolen@mathcs.emory.edu

**John Willis**

Affiliation:
Department of Mathematics, University of South Carolina, 1523 Greene Street, Columbia, South Carolina 29208

Email:
willisj5@mailbox.sc.edu

DOI:
https://doi.org/10.1090/S0002-9939-2014-12289-1

Received by editor(s):
March 25, 2013

Received by editor(s) in revised form:
March 26, 2013, and June 19, 2013

Published electronically:
October 29, 2014

Communicated by:
Ken Ono

Article copyright:
© Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.