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Elliptic Zeta functions and equivariant functions

  • Abdellah Sebbar,
    Department of Mathematics and Statistics, University of Ottawa, Ottawa Ontario K1N 6N5
  • Isra Al-Shbeil,
    Department of Mathematics and Statistics, University of Ottawa, Ottawa Ontario K1N 6N5
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Abstract

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: modular form, equivariant function, elliptic zeta function modular form, equivariant function, elliptic zeta function
MSC Classifications: 11F12, 35Q15, 32L10 show english descriptions Automorphic forms, one variable
Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]
Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
11F12 - Automorphic forms, one variable
35Q15 - Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]
32L10 - Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
 

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