There are many results in the literature concerning power values, equal values or more generally, polynomial values of lattice point counting polynomials. In this paper, we prove various finiteness results for polynomial values of polynomials counting the lattice points on the surface of an [Formula: see text]-dimensional cube, pyramid and simplex.

中文翻译：

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表面点计数多项式的多项式值

文献中有许多关于幂值、等值或更一般地格点计数多项式的多项式值的结果。在本文中，我们证明了多项式的多项式值的各种有限性结果，该多项式对 [公式：参见文本] 维立方体、金字塔和单纯形表面上的格点进行计数。