Timeline for A reference for this possibly well-known fact concerning the Kakeya conjecture?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2013 at 10:37 | vote | accept | js21 | ||
| Jul 24, 2013 at 18:15 | answer | added | Terry Tao | timeline score: 8 | |
| Jul 24, 2013 at 17:01 | comment | added | js21 | However, the quote above confirms that (a) such a reformulation in terms of arithmetic progressions actually exist and (b) it is "well known" to at least two experts (Katz&Tao ...). | |
| Jul 24, 2013 at 16:52 | comment | added | js21 | I think you refer to the sentence "Indeed,the Kakeya conjecture can be reformulated in terms of arithmetic progressions, and this can be used to connect the Kakeya conjecture to several difficult conjectures in number theory such as the Montgomery conjectures for generic Dirichlet series. We will not discuss this connection here, but refer the reader to [4]" from Katz&Tao. But as far as I can see, the reference given describes the connection between Dirichlet polynomials and Kakeya, but not the reformulation of Kakeya in terms of arithmetic progressions. | |
| Jul 24, 2013 at 16:27 | comment | added | Joseph O'Rourke | Katz & Tao's survey article cites this (but I don't know if it contains your specific point): J. Bourgain: Harmonic Analysis and Combinatorics: How Much May They Contribute to Each Other?, in Mathematics: Frontiers and Perspectives, V. Arnold, M. Atiyah, P. Lax, B. Mazur, eds., AMS 2000. | |
| Jul 24, 2013 at 15:49 | history | asked | js21 | CC BY-SA 3.0 |