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We consider the Hermitian Eisenstein series $E^{(\mathbb{K})}_k$ of degree $2$ and weight $k$ associated with an imaginary-quadratic number field $\mathbb{K}$ and determine the influence of $\mathbb{K}$ on the arithmetic and the growth of its Fourier coefficients. We find that they satisfy the identity $E^{{(\mathbb{K})}^2}_4 = E^{{(\mathbb{K})}}_8$, which is well-known for Siegel modular forms of degree $2$, if and only if $\mathbb{K} = \mathbb{Q} (\sqrt{-3})$. As an application, we show that the Eisenstein series $E^{(\mathbb{K})}_k$, $k=4,6,8,10,12$ are algebraically independent whenever $\mathbb{K}\neq \mathbb{Q}(\sqrt{-3})$. The difference between the Siegel and the restriction of the Hermitian to the Siegel half-space is a cusp form in the Maass space that does not vanish identically for sufficiently large weight; however, when the weight is fixed, we will see that it tends to $0$ as the discriminant tends to $-\infty$. Finally, we show that these forms generate the space of cusp forms in the Maass Spezialschar as a module over the Hecke algebra as $\mathbb{K}$ varies over imaginary-quadratic number fields., Comment: 15 pages

We use Borcherds products and their restrictions to Hirzebruch-Zagier curves to determine generators and relations for the graded rings of Hilbert modular forms for the fields $\mathbb{Q}(\sqrt{29})$ and $\mathbb{Q}(\sqrt{37})$. These seem to be the first cases where the graded ring can be computed despite obstructions to the existence of Borcherds products with arbitrary divisors., Comment: 18 pages. v2 fixes some typos

We give expressions for the Serre derivatives of Eisenstein and Poincar�� series as well as their Rankin-Cohen brackets with arbitrary modular forms in terms of the Poincar�� averaging construction, and derive several identities for the Ramanujan tau function as applications., 11 pages

We demonstrate an application of the Futamura Projections to human-computer interaction, and particularly to staging human-computer dialogs. Specifically, by providing staging analogs to the classical Futamura Projections, we demonstrate that the Futamura Projections can be applied to the staging of human-computer dialogs in addition to the execution of programs., Comment: 13 pages, 6 figures, and 3 tables

We extend the author's earlier computation and give coefficient formulas for the (quasimodular) Poincar�� square series of weight 3/2 and weight 2 for the dual Weil representation for an even lattice., 17 pages