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Trudy Mat. Inst. Steklova, 2015, Volume 289, Pages 318–327 (Mi tm3616)  

This article is cited in 12 scientific papers (total in 12 papers)

On sums of Szemerédi–Trotter sets

I. D. Shkredovab

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433


DOI: https://doi.org/10.1134/S0371968515020181

Full text: PDF file (194 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 300–309

Bibliographic databases:

UDC: 511.34+511.212
Received: January 15, 2015

Citation: I. D. Shkredov, “On sums of Szemerédi–Trotter sets”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Trudy Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 318–327; Proc. Steklov Inst. Math., 289 (2015), 300–309

Citation in format AMSBIB
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\by I.~D.~Shkredov
\paper On sums of Szemer\'edi--Trotter sets
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 318--327
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3616}
\crossref{https://doi.org/10.1134/S0371968515020181}
\elib{https://elibrary.ru/item.asp?id=23738476}
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\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 289
\pages 300--309
\crossref{https://doi.org/10.1134/S0081543815040185}
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  • https://doi.org/10.1134/S0371968515020181
  • http://mi.mathnet.ru/eng/tm/v289/p318

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Konyagin, I. D. Shkredov, “On sum sets of sets having small product set”, Proc. Steklov Inst. Math., 290:1 (2015), 288–299  mathnet  crossref  crossref  isi  elib  elib
    2. I. D. Shkredov, “On a question of A. Balog”, Pacific J. Math., 280:1 (2016), 227–240  mathnet  crossref  mathscinet  zmath  isi  scopus
    3. S. V. Konyagin, I. D. Shkredov, “New results on sums and products in $\mathbb R$”, Proc. Steklov Inst. Math., 294 (2016), 78–88  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. O. E. Raz, M. Sharir, I. D. Shkredov, “On the number of unit-area triangles spanned by convex grids in the plane”, Comput. Geom.-Theory Appl., 62 (2017), 25–33  crossref  mathscinet  zmath  isi  scopus
    5. I. D. Shkredov, “Some Remarks on the Balog–Wooley Decomposition Theorem and Quantities $D^{+}$, $D^\times$”, Proc. Steklov Inst. Math., 298, suppl. 1 (2017), 74–90  mathnet  crossref  crossref  mathscinet  isi  elib
    6. I. D. Shkredov, “Some remarks on sets with small quotient set”, Sb. Math., 208:12 (2017), 1854–1868  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. B. Murphy, O. Roche-Newton, I. D. Shkredov, “Variations on the sum-product problems II”, SIAM Discret. Math., 31:3 (2017), 1878–1894  crossref  mathscinet  zmath  isi  scopus
    8. G. Shakan, “On higher energy decompositions and the sum-product phenomenon”, Math. Proc. Camb. Philos. Soc., 167:3 (2019), 599–617  crossref  mathscinet  isi
    9. K. I. Olmezov, “Sharpening an Estimate of the Size of the Sumset of a Convex Set”, Math. Notes, 107:6 (2020), 954–957  mathnet  crossref  crossref  mathscinet  isi  elib
    10. K. I. Olmezov, A. S. Semchankau, I. D. Shkredov, “On Popular Sums and Differences for Sets with Small Multiplicative Doubling”, Math. Notes, 108:4 (2020), 557–565  mathnet  crossref  crossref  mathscinet  isi  elib
    11. M. Rudnev, I. D. Shkredov, S. Stevens, “On the energy variant of the sum-product conjecture”, Rev. Mat. Iberoam., 36:1 (2020), 207–232  crossref  mathscinet  isi
    12. K. I. Olmezov, “An Elementary Analog of the Operator Method in Additive Combinatorics”, Math. Notes, 109:1 (2021), 110–119  mathnet  crossref  crossref  mathscinet  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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