摘要翻译：
我们给出了与黎曼假设的Nyman-Beurling方法有关的、由V.I.Vasyunin研究过的一类阶跃函数的完整分类。等价地，我们完整地描述了当阶乘积的某些比率序列总是积分时。从本质上说，一旦有了一定的观察，这就归结为Beukers和Heckman对超几何函数nF_{n-1}的单数分类的应用。我们还注意到循环商奇点分类的应用。
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英文标题：
《Factorial ratios, hypergeometric series, and a family of step functions》
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作者：
Jonathan Bober
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Combinatorics        组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
  We give a complete classification of a certain family of step functions related to the Nyman--Beurling approach to the Riemann hypothesis and previously studied by V. I. Vasyunin. Equivalently, we completely describe when certain sequences of ratios of factorial products are always integral. Essentially, once certain observations are made, this comes down to an application of Beukers and Heckman's classification of the monodromy of the hypergeometric function nF_{n-1}. We also note applications to the classification of cyclic quotient singularities.
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PDF链接：
https://arxiv.org/pdf/0709.1977