On Equivariant Elliptic Genera of Toric Calabi-Yau 3-folds

We show that equivariant elliptic genera of toric Calabi-Yau 3-folds are generalized weak Jacobi forms. We also introduce a notion of averaged equivariant elliptic genera of toric Calabi-Yau 3-folds, and show that they are ordinary weak Jacobi forms given by an explicit formula predicted by Eguchi and Sugawara.