An improved incidence bound for fields of prime order
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Bourgain, 2009, On a variant of sum–product estimates and explicit exponential sum bounds in prime fields, Math. Proc. Cambridge Philos. Soc., 146, 1, 10.1017/S0305004108001230
Bourgain, 2004, A sum–product estimate in finite fields and applications, Geom. Funct. Anal., 14, 27, 10.1007/s00039-004-0451-1
Elekes, 1997, On the number of sums and products, Acta. Arith., 81, 365, 10.4064/aa-81-4-365-367
Helfgott, 2011, An explicit incidence theorem in Fp, Mathematika, 57, 135, 10.1112/S0025579310001208
Jones, 2011, Explicit incidence bounds over general finite fields, Acta Arith., 150, 241, 10.4064/aa150-3-3
Konyagin, 2013, On new sum–product type estimates, SIAM J. Discrete Math., 27, 973, 10.1137/120886418
Li, 2011, An improved sum–product estimate for general finite fields, SIAM J. Discrete Math., 25, 10.1137/110823122
Li, 2012, Convexity and a sum–product type estimate, Acta. Arith., 156, 247, 10.4064/aa156-3-3
Rudnev, 2012, An improved sum–product inequality in fields of prime order, Int. Math. Res. Not., 16, 3693, 10.1093/imrn/rnr158
Solymosi, 2005, On the number of sums and products, Bull. Lond. Math. Soc., 37, 491, 10.1112/S0024609305004261
Solymosi, 2009, Bounding multiplicative energy by the sumset, Adv. Math., 222, 402, 10.1016/j.aim.2009.04.006
J. Solymosi, T. Tao, An incidence theorem in higher dimensions, 2011. Preprint arxiv:1103.2926.
Szemerédi, 1983, Extremal problems in discrete geometry, Combinatorica, 3, 381, 10.1007/BF02579194
Tao, 2006
C. Tóth, The Szemerédi–Trotter theorem in the complex plane, 2005. Preprint arXiv:0305283v3.
Vinh, 2011, The Szemerédi–Trotter theorem and the sum–product estimate in finite fields, European J. Combin., 32, 1177, 10.1016/j.ejc.2011.06.008
