Timeline for Minimum distance between adjacent concentric circles that cross integer lattice points
Current License: CC BY-SA 3.0
7 events
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| Aug 17, 2011 at 22:16 | vote | accept | wolfrevo | ||
| Aug 17, 2011 at 4:33 | comment | added | Noam D. Elkies | @D.Zare: Halberstam's paper notes this connection too (though the best exponent known in 1983 was probably worse). | |
| Aug 17, 2011 at 4:12 | comment | added | Douglas Zare | You may want to look up the Gauss Circle Problem, which asks for the number of lattice points in a circle of radius $r$ centered at the origin, $\pi r^2 + E(r)$. Upper bounds on the error estimates give you crude upper bounds on the gaps between distances to lattice points. For example, the bound $E(r) = O(r^{131/208})$ tells you that $\Delta r_i = O(r_i^{131/208}/r_i) = O(r_i^{-77/208})$. The best this could possibly do, if someone solved the Gauss Circle Problem, would be a little worse than $O(r_i^{-1/2})$. However, the methods may be of interest. | |
| Aug 17, 2011 at 3:01 | answer | added | Noam D. Elkies | timeline score: 12 | |
| Aug 17, 2011 at 2:34 | history | edited | wolfrevo | CC BY-SA 3.0 |
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| Aug 17, 2011 at 2:03 | history | edited | wolfrevo | CC BY-SA 3.0 |
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| Aug 17, 2011 at 1:53 | history | asked | wolfrevo | CC BY-SA 3.0 |