Geodesic
New bounds on cap sets
Bateman, Michael 1   ; Katz, Nets 2
1 Department of Mathematics, UCLA, Los Angeles, California 90095
2 Department of Mathematics, Indiana University, Bloomington, Indiana 47405-7000
Journal of the American Mathematical Society, Tome 25 (2012) no. 2, pp. 585-613 Cet article a éte moissonné depuis la source American Mathematical Society

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We provide an improvement over Meshulam’s bound on cap sets in $F_3^N$. We show that there exist universal $\epsilon >0$ and $C>0$ so that any cap set in $F_3^N$ has size at most $C {3^N \over N^{1+\epsilon }}$. We do this by obtaining quite strong information about the additive combinatorial properties of the large spectrum.
DOI : 10.1090/S0894-0347-2011-00725-X

Bateman, Michael  1   ; Katz, Nets  2

1 Department of Mathematics, UCLA, Los Angeles, California 90095
2 Department of Mathematics, Indiana University, Bloomington, Indiana 47405-7000 
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Bateman, Michael; Katz, Nets. New bounds on cap sets. Journal of the American Mathematical Society, Tome 25 (2012) no. 2, pp. 585-613. doi: 10.1090/S0894-0347-2011-00725-X

[1] Croot, Ernie, Sisask, Olof A probabilistic technique for finding almost-periods of convolutions Geom. Funct. Anal. 2010 1367 1396

[2] Katz, Nets Hawk, Koester, Paul On additive doubling and energy SIAM J. Discrete Math. 2010 1684 1693

[3] Meshulam, Roy On subsets of finite abelian groups with no 3-term arithmetic progressions J. Combin. Theory Ser. A 1995 168 172

[4] Ruzsa, Imre Z. An analog of Freiman’s theorem in groups Astérisque 1999

[5] Sanders, T. A note on Freĭman’s theorem in vector spaces Combin. Probab. Comput. 2008 297 305

[6] Schoen, Tomasz Near optimal bounds in Freiman’s theorem Duke Math. J. 2011 1 12

[7] Shkredov, I. D. On sets of large trigonometric sums Izv. Ross. Akad. Nauk Ser. Mat. 2008 161 182

[8] Tao, Terence, Vu, Van Additive combinatorics 2006

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