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Equivariant Forms: Structure and Geometry

Published online by Cambridge University Press:  20 November 2018

Abdelkrim Elbasraoui  and
Abdellah Sebbar
Abdelkrim Elbasraoui
Affiliation:
Centre de recherches mathématiques, Université de Montréal, Montréal, QC H3C 3J7 e-mail: elbasrao@crm.umontreal.ca CICMA, Concordia University, Montréal, QC H3G 1M8 e-mail: elbasrao@crm.umontreal.ca
Abdellah Sebbar
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5
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Abstract.

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In this paper we study the notion of equivariant forms introduced in the authors' previous works. In particular, we completely classify all the equivariant forms for a subgroup of $\text{S}{{\text{L}}_{2\left( \mathbb{Z} \right)}}$ by means of the cross-ratio, weight 2 modular forms, quasimodular forms, as well as differential forms of a Riemann surface and sections of a canonical line bundle.

Keywords

11F11equivariant formsmodular formsSchwarz derivativecross-ratiodifferential forms

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 520 - 533
Copyright
Copyright © Canadian Mathematical Society 2013

References

[1] Brady, M., Meromorphic solutions of a system of functional equations involving the modular group. Proc. Amer. Math. Soc. 30 (1971), 271–277. http://dx.doi.org/10.1090/S0002-9939-1971-0280712-5 Google Scholar
[2] El basraoui, A. and Sebbar, A., Rational equivariant forms. Int. J. Number Theory, to appear. http://dx.doi.org/10.1142/S1793042112500571 Google Scholar
[3] Heins, M., On the pseudo-periods of the Weierstrass zeta functions. II. Nagoya Math. J. 30 (1967), 113–119.Google Scholar
[4] Kaneko, M. and Zagier, D., A generalized Jacobi theta function and quasimodular forms. In: The moduli space of curves (Texel Island, 1994), Progr. Math., 129, Birkh¨auser Boston, Boston, MA, 1995, pp. 165–172.Google Scholar
[5] Knopp, M. and Mason, G., Generalized modular forms. J. Number Theory 99 (2003), no. 1, 1–28. http://dx.doi.org/10.1016/S0022-314X(02)00065-3 Google Scholar
[6] Sebbar, A. and Sebbar, A., Equivariant functions and integrals of elliptic functions. GeoDedicata, m., to appear. http://dx.doi.org/10.1007/S10711-011-9688-7 Google Scholar
[7] Smart, J. R., On meromorphic functions commuting with elements of a function group. Proc. Amer. Math. Soc. 33 (1972), 343–348. http://dx.doi.org/10.1090/S0002-9939-1972-0293086-1 Google Scholar