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Elliptic Zeta Functions and Equivariant Functions

Published online by Cambridge University Press:  20 November 2018

Abdellah Sebbar  and
Isra Al-Shbeil
Abdellah Sebbar
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa ON K1N 6N5, e-mail: asebbar@uottawa.ca
Isra Al-Shbeil
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa ON K1N 6N5, e-mail: ialsh010@uottawa.ca
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Abstract

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In this paper we establish a close connection between three notions attached to a modular subgroup, namely, the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action of the modular subgroup, and the set of elliptic zeta functions generalizing the Weierstrass zeta functions. In particular, we show that the equivariant functions can be parameterized by modular objects as well as by elliptic objects.

Keywords

11F1235Q1532L10modular formequivariant functionelliptic zeta function

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 2 , 01 June 2018 , pp. 376 - 389
Copyright
Copyright © Canadian Mathematical Society 2018

References

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