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Let $ H_g$ be the Siegel upper-half plance of genus $ g$ , and $ \Gamma=Sp_{2g}(\mathbb{Z})$ the full modular group of genus $ g$ . As usual, we can define non-holomorphic Eisenstein and Poincare series as $ $ E^{(g)}_k(Z,s)=\sum_\gamma \delta(\gamma Z)^s j(\gamma,Z)^{-k}$ $ $ $ P^{(g)}_{A,k}(Z,s)=\sum_\gamma \delta(\gamma Z)^s j(\gamma,Z)^{-k}e^{2\pi i \sigma(A\gamma Z)}$ $ where $Read more