2019/01/16 by K. Soundararajan, Soundararajan, K. · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1901.05133
31 pages
arxiv created 2019/01/16 · openalex publication_date 2019/01/16 · arxiv updated 2019/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper describes a new approach to classifying integral factorial ratio, obtaining in particular a direct proof of a result of Bober. These results generalize an observation going back to Chebyshev that (30n)!n!/((15n)!(10n)!(6n)!) is an integer for all n. Due to the work of Rodriguez-Villegas and Beukers and Heckman, this problem is closely related to classifying hypergeometric functions with finite monodromy groups, and the result of Bober was originally derived as a consequence of the work of Beukers--Heckman. The new proof is elementary and makes partial progress on other related questions.