Pair correlation and twin primes revisited
We establish a connection between the conjectural two-over-two ratios formula for the Riemann zetafunction and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. Th...
| Main Authors: | , |
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| Format: | Journal article |
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Royal Society
2016
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| _version_ | 1826258330680557568 |
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| author | Conrey, B Keating, J |
| author_facet | Conrey, B Keating, J |
| author_sort | Conrey, B |
| collection | OXFORD |
| description | We establish a connection between the conjectural two-over-two ratios formula for the Riemann zetafunction and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. |
| first_indexed | 2024-03-06T18:32:18Z |
| format | Journal article |
| id | oxford-uuid:0a113735-33b9-4026-943b-504a0ba01c43 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:32:18Z |
| publishDate | 2016 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:0a113735-33b9-4026-943b-504a0ba01c432022-03-26T09:21:50ZPair correlation and twin primes revisitedJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0a113735-33b9-4026-943b-504a0ba01c43Symplectic Elements at OxfordRoyal Society2016Conrey, BKeating, JWe establish a connection between the conjectural two-over-two ratios formula for the Riemann zetafunction and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe. |
| spellingShingle | Conrey, B Keating, J Pair correlation and twin primes revisited |
| title | Pair correlation and twin primes revisited |
| title_full | Pair correlation and twin primes revisited |
| title_fullStr | Pair correlation and twin primes revisited |
| title_full_unstemmed | Pair correlation and twin primes revisited |
| title_short | Pair correlation and twin primes revisited |
| title_sort | pair correlation and twin primes revisited |
| work_keys_str_mv | AT conreyb paircorrelationandtwinprimesrevisited AT keatingj paircorrelationandtwinprimesrevisited |