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Article overview
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On an application of Guth-Katz theorem | Alex Iosevich
; Misha Rudnev
; Oliver Roche-Newton
; | Date: |
7 Mar 2011 | Abstract: | We prove that for some universal $c$, a non-collinear set of $N>frac{1}{c}$
points in the Euclidean plane determines at least $c frac{N}{log N}$ distinct
areas of triangles with one vertex at the origin, as well as at least $c
frac{N}{log N}$ distinct dot products.
This in particular implies a sum-product bound $$ |Acdot Apm Acdot A|geq
cfrac{|A|^2}{log |A|} $$ for a discrete $A subset {mathbb R}$. | Source: | arXiv, 1103.1354 | Services: | Forum | Review | PDF | Favorites |
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