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Factorial ratios, hypergeometric series, and a family of step function | | Jonathan Bober
; | | Date: |
13 Sep 2007 | | Abstract: | 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. | | Source: | arXiv, 0709.1977 | | Services: | Forum | Review | PDF | Favorites | |
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