1. CMB 2011 (vol 55 pp. 67)
|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 leastÂ 4.
Categories:11F20, 11F12, 17B60
2. CMB 2001 (vol 44 pp. 282)
|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.
3. CMB 1999 (vol 42 pp. 263)
|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