Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers
The occurrence and frequency of a phenomenon of resonance (namely the coalescence of some Dubrovin canonical coordinates) in the locus of Small Quantum Cohomology of complex Grassmannians is studied. It is shown that surprisingly this frequency is strictly subordinate and highly influenced by the di...
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| description | The occurrence and frequency of a phenomenon of resonance (namely the coalescence of some Dubrovin canonical coordinates) in the locus of Small Quantum Cohomology of complex Grassmannians is studied. It is shown that surprisingly this frequency is strictly subordinate and highly influenced by the distribution of prime numbers. Two equivalent formulations of the Riemann Hypothesis are given in terms of numbers of complex Grassmannians without coalescence: the former as a constraint on the disposition of singularities of the analytic continuation of the Dirichlet series associated to the sequence counting non-coalescing Grassmannians, the latter as asymptotic estimate (whose error term cannot be improved) for their distribution function. |
| doi_str_mv | 10.48550/arxiv.1608.06868 |
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It is shown that surprisingly this frequency is strictly subordinate and highly influenced by the distribution of prime numbers. Two equivalent formulations of the Riemann Hypothesis are given in terms of numbers of complex Grassmannians without coalescence: the former as a constraint on the disposition of singularities of the analytic continuation of the Dirichlet series associated to the sequence counting non-coalescing Grassmannians, the latter as asymptotic estimate (whose error term cannot be improved) for their distribution function.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1608.06868</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Coalescing ; Dirichlet problem ; Distribution functions ; Formulations ; Homology ; Mathematical analysis ; Mathematics - Algebraic Geometry ; Mathematics - Mathematical Physics ; Mathematics - Number Theory ; Physics - Mathematical Physics ; Prime numbers ; Series (mathematics) ; Singularities</subject><ispartof>arXiv.org, 2016-09</ispartof><rights>2016. 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| subjects | Coalescing Dirichlet problem Distribution functions Formulations Homology Mathematical analysis Mathematics - Algebraic Geometry Mathematics - Mathematical Physics Mathematics - Number Theory Physics - Mathematical Physics Prime numbers Series (mathematics) Singularities |
| title | Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers |
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