Geodesic
On sums of Szemerédi–Trotter sets
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 318-327 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove new general results on sumsets and difference sets for sets of the Szemerédi–Trotter type. This family includes convex sets, sets with small multiplicative doubling, images of sets under convex/concave maps and others. 
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     author = {I. D. Shkredov},
     title = {On sums of {Szemer\'edi{\textendash}Trotter} sets},
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I. D. Shkredov. On sums of Szemerédi–Trotter sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 318-327. http://geodesic.mathdoc.fr/item/TM_2015_289_a17/

[1] Elekes G., Nathanson M. B., Ruzsa I. Z., “Convexity and sumsets”, J. Number Theory, 83:2 (2000), 194–201 | DOI | MR | Zbl

[2] Garaev M. Z., “O nizhnikh otsenkakh $L_1$-normy nekotorykh eksponentsialnykh summ”, Mat. zametki, 68:6 (2000), 842–850 | DOI | MR | Zbl

[3] Garaev M. Z., Kueh K-L., “On cardinality of sumsets”, J. Aust. Math. Soc., 78:2 (2005), 221–226 | DOI | MR | Zbl

[4] Hegyvári N., “On consecutive sums in sequences”, Acta math. Hung., 48 (1986), 193–200 | DOI | MR | Zbl

[5] Iosevich A., Konyagin S., Rudnev M., Ten V., “Combinatorial complexity of convex sequences”, Discrete Comput. Geom., 35:1 (2006), 143–158 | DOI | MR | Zbl

[6] Jones T. G. F., Roche-Newton O., “Improved bounds on the set $A(A+1)$”, J. Comb. Theory A, 120:3 (2013), 515–526 | DOI | MR | Zbl

[7] Konyagin S. V., Rudnev M., “On new sum–product type estimates”, SIAM J. Discrete Math., 27:2 (2013), 973–990 | DOI | MR | Zbl

[8] Li L., On a theorem of Schoen and Shkredov on sumsets of convex sets, E-print, 2011, arXiv: 1108.4382v1[math.CO]

[9] Li L., Roche-Newton O., “Convexity and a sum-product type estimate”, Acta arith., 156:3 (2012), 247–255 | DOI | MR | Zbl

[10] Murphy B., Roche-Newton O., Shkredov I., Variations on the sum-product problem, E-print, 2014, arXiv: 1312.6438v2[math.CO] | MR

[11] Schoen T., “On convolutions of convex sets and related problems”, Can. Math. Bull., 57:4 (2014), 877–883 | DOI | MR | Zbl

[12] Schoen T., Shkredov I. D., “On sumsets of convex sets”, Comb. Probab. Comput., 20:5 (2011), 793–798 | DOI | MR | Zbl

[13] Schoen T., Shkredov I. D., “Higher moments of convolutions”, J. Number Theory, 133:5 (2013), 1693–1737 | DOI | MR | Zbl

[14] Shkredov I. D., “Some new inequalities in additive combinatorics”, Moscow J. Comb. Number Theory, 3 (2013), 189–239 | MR | Zbl

[15] Shkredov I. D., “Neskolko novykh rezultatov o starshikh energiyakh”, Tr. Mosk. mat. o-va, 74, no. 1, 2013, 35–73 | MR | Zbl

[16] Solymosi J., “Sumas contra productos”, Gac. R. Soc. Mat. Esp., 12:4 (2009), 707–719 | MR | Zbl

[17] Tao T., Vu V. H., Additive combinatorics, Cambridge Univ. Press, Cambridge, 2006 | MR | Zbl