Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On a certain class of modular functions


Author: Winfried Kohnen
Journal: Proc. Amer. Math. Soc. 133 (2005), 65-70
MSC (2000): Primary 11F11
DOI: https://doi.org/10.1090/S0002-9939-04-07450-7
Published electronically: May 12, 2004
MathSciNet review: 2085154
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a characterization of those meromorphic modular functions on a subgroup of finite index of the full modular group whose divisors are supported at the cusps, in terms of the growth of the exponents of their infinite product expansions.


References [Enhancements On Off] (What's this?)

  • 1. J. H. Bruinier, W. Kohnen and K. Ono: The arithmetic of the values of modular functions and the divisors of modular forms, to appear in Compositio Math.
  • 2. W. Eholzer and N.-P. Skoruppa: Product expansions of conformal characters, Phys. Lett. B. 388 (1996), 82-89. MR 97k:81132
  • 3. G. H. Hardy and E. M. Wright: An Introduction to the Theory of Numbers, Oxford University Press, Oxford, 1975. MR 81i:10002
  • 4. E. Hecke: Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik, In: Erich Hecke, Mathematische Werke (ed.: Akademie der Wissenschaften Göttingen), pp. 461-486, Vandenhoeck & Ruprecht: Göttingen, 1959. MR 21:3303
  • 5. D. S. Kubert and S. Lang: Modular units, Grundlehren der Mathematischen Wissenschaften, no. 244, Springer-Verlag, Berlin, Heidelberg, New York, 1981. MR 84h:12009
  • 6. S. Lang: Introduction to Modular Forms, Grundlehren der Mathematischen Wissenschaften, no. 222, Springer-Verlag, Berlin, Heidelberg, New York, 1976. MR 55:2751
  • 7. H. Maass: Lectures on Modular Functions of One Complex Variable, Tata Institute of Fundamental Research, Bombay, 1964 (revised 1983). MR 85g:11034
  • 8. Y. Martin: Multiplicative $\eta$-quotients, Trans. Amer. Math. Soc. 348, no. 12 (1996), 4825-4856. MR 97d:11070
  • 9. R. A. Rankin: Modular Forms and Functions, Cambridge University Press, Cambridge, 1977. MR 58:16518

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F11

Retrieve articles in all journals with MSC (2000): 11F11


Additional Information

Winfried Kohnen
Affiliation: Mathematisches Institut, Universität Heidelberg, INF 288, D-69120 Heidelberg, Germany
Email: winfried@mathi.uni-heidelberg.de

DOI: https://doi.org/10.1090/S0002-9939-04-07450-7
Received by editor(s): February 12, 2003
Received by editor(s) in revised form: July 9, 2003, and October 27, 2003
Published electronically: May 12, 2004
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society