Hostname: page-component-89b8bd64d-n8gtw Total loading time: 0 Render date: 2026-05-10T14:24:43.785Z Has data issue: false hasContentIssue false
  • English
  • Français

Cusp Forms Like Δ

Published online by Cambridge University Press:  20 November 2018

C. J. Cummins
C. J. Cummins*
Affiliation:
Department of Mathematics and Statistics, Concordia University, Montréal, QC, H3G 1M8 e-mail: cummins@mathstat.concordia.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Let $f$ be a square-free integer and denote by ${{\Gamma }_{0}}{{\left( f \right)}^{+}}$ the normalizer of ${{\Gamma }_{0}}\left( f \right)$ in $\text{SL}\left( 2,\,\mathbb{R} \right)$ . We find the analogues of the cusp form $\Delta$ for the groups ${{\Gamma }_{0}}{{\left( f \right)}^{+}}$ .

Keywords

11F0311F2230F35

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 53 - 62
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Atkin, A. O. L and Lehner, J., Hecke operators for Γ 0(m). Math. Ann. 185(1970) 134–160.Google Scholar
[2] Biagioli, A. J. F., The construction of modular forms as products of transforms of the Dedekind eta function. Acta Arith. 54(1990), no. 4, 273–300.Google Scholar
[3] Conway, J. H., Understanding groups like Γ 0(N). In: Groups, difference sets, and the Monster, Ohio State Univ. Math. Res. Inst. Publ. 4, de Gruyter, Berlin, 1996, pp. 327–343.Google Scholar
[4] Cummins, C. J., Congruence subgroups of groups commensurable with PSL(2, ℤ) of genus 0 and 1. Experiment. Math. 13(2004), no. 3, 361–382.Google Scholar
[5] Dummit, D., Kisilevsky, H., and McKay, J., Multiplicative products of η-functions. In: Finite groups—coming of age, Contemp. Math. 45, American Mathemtical Society, Providence, RI, 1985, pp. 89–98.Google Scholar
[6] Gordon, B. and Ono, K., Divisibility of certain partition functions by powers of primes. Ramanujan J. 1(1997), no. 1, 25–34.Google Scholar
[7] Helling, H., Bestimmung der Kommensurabilitätsklasse der Hilbertschen Modulgruppe. Math. Z. 92(1966), 269–280.Google Scholar
[8] Knopp, M. I., Modular functions in analytic number theory. Markham Publishing Co., Chicago, Ill., 1970.Google Scholar
[9] Newman, M., Construction and application of a class of modular functions. Proc. London. Math. Soc. (3) 7(1957), 334–350.Google Scholar
[10] Newman, M, Construction and application of a class of modular functions. II. Proc. London Math. Soc., (3) 9(1959), 373–387.Google Scholar
[11] Petersson, H., Über Modulfunktionen und Partitionenprobleme. Abh. Deutsch. Akad.Wiss. Berlin. Kl. Math. Allg. Nat. 1954, no. 2, 59pp.Google Scholar
[12] Rademacher, H. Zur Theorie der Modulfunktionen. J. Reine Angew. Math. 167(1932), 312–336.Google Scholar
[13] Shimura, G., Introduction to the arithmetic theory of automorphic functions. Publications of the Mathematical Society of Japan 11, Princeton University Press, Princeton, NJ, 1971.Google Scholar