Let R be a positively graded algebra over a field $\mathbb{k}$. We say that R is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. Such rings arise naturally in commutative algebra, numerical semigroup theory and Ehrhart theory. If R is standard graded, we prove that, under the additional hypothesis that R is Koszul or has an irreducible h-polynomial, Hilbert-cyclotomic algebras coincide with complete intersections. In the Koszul case, this is a consequence of some classical results about the vanishing of deviations of a graded algebra.

中文翻译：

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圈数希尔伯特级数的渐变代数

令R是一个场上的正阶代数$\mathbb{ķ}$。我们说，如果R的简化希尔伯特级数的分子的所有根都在单位圆上，则R是希尔伯特环的。这样的环在交换代数，数值半群论和Ehrhart理论中自然而然地出现。如果R是标准等级的，我们证明在R为Koszul或具有不可约h多项式的附加假设下，希尔伯特-环代数与完全交点重合。在Koszul案例中，这是一些有关渐进代数偏差消失的经典结果的结果。