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Search: MSC category 11F12 ( Automorphic forms, one variable )

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1. CMB Online first

Sebbar, Abdellah; Al-Shbeil, Isra
Elliptic Zeta functions and equivariant functions
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
Categories:11F12, 35Q15, 32L10

2. CMB 2011 (vol 55 pp. 67)

Cummins, C. J.; Duncan, J. F.
An $E_8$ Correspondence for Multiplicative Eta-Products
We describe an $E_8$ correspondence for the multiplicative eta-products of weight at least $4$.

Keywords:We describe an E8 correspondence for the multiplicative eta-products of weight at least 4.
Categories:11F20, 11F12, 17B60

3. CMB 2001 (vol 44 pp. 282)

Lee, Min Ho; Myung, Hyo Chul
Hecke Operators on Jacobi-like Forms
Jacobi-like forms for a discrete subgroup $\G \subset \SL(2,\mbb R)$ are formal power series with coefficients in the space of functions on the Poincar\'e upper half plane satisfying a certain functional equation, and they correspond to sequences of certain modular forms. We introduce Hecke operators acting on the space of Jacobi-like forms and obtain an explicit formula for such an action in terms of modular forms. We also prove that those Hecke operator actions on Jacobi-like forms are compatible with the usual Hecke operator actions on modular forms.

Categories:11F25, 11F12

4. CMB 1999 (vol 42 pp. 263)

Choie, Youngju; Lee, Min Ho
Mellin Transforms of Mixed Cusp Forms
We define generalized Mellin transforms of mixed cusp forms, show their convergence, and prove that the function obtained by such a Mellin transform of a mixed cusp form satisfies a certain functional equation. We also prove that a mixed cusp form can be identified with a holomorphic form of the highest degree on an elliptic variety.

Categories:11F12, 11F66, 11M06, 14K05

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