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New Encounters in Combinatorial Number Theory: From the Kakeya Problem to Cryptography

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Part of the book series: Mathematical Physics Studies ((MPST,volume 27))

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References

  1. A.S. Besicovitch: Math. Z. 27, 312 (1928)

    Article  MathSciNet  Google Scholar 

  2. J. Bourgain: GAFA 1, 202, 147 (1991)

    Article  MathSciNet  Google Scholar 

  3. J. Bourgain: Some new estimates on oscillatory integrals. In: Essays in Fourier Analysis in honor of E.M. Stein (Princeton University Press 1995) pp 83–112

    Google Scholar 

  4. J. Bourgain: Λp sets in analysis: results, problems and related aspects. In: Handbook of the geometry of Banach spaces, vol I (North-Holland, Amsterdam 2001) pp 195–232

    Google Scholar 

  5. J. Bourgain: GAFA 15, 1 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Bourgain: JAMS 18, 477 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Bourgain: Geom. Funct. Anal. 13 no 2, 334 (2003)

    MathSciNet  MATH  Google Scholar 

  8. J. Bourgain: Harmonic analysis and combinatorics: how much may they contribute to each other? In: Mathematics: frontiers and perspectives (American Math. Soc., Providence, RI, 2000) pp 13–32

    Google Scholar 

  9. W.D. Banks, A. Conflitti, J.B. Friedlander, I.E. Shparlinski: Compos. Math. 140 no 1, 15 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. R.C. Baker, G. Harman: Acta Arith. 83 no 4, 331 (1998)

    MathSciNet  MATH  Google Scholar 

  11. J. Bourgain, S.V. Konyagin: C.R.Math. Acad. Sci. Paris 337 no 2, 75 (2003)

    MathSciNet  MATH  Google Scholar 

  12. J. Bourgain, N. Katz, T. Tao: GAFA 14 no 1, 27 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. K.L. Clarkson. H. Edelsbrunner et al: Discrete Comput. Geom. 5 no 2, 99 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Canetti, J. Friedlander et al: Israel J. Math. 120, 23 (2000)

    MathSciNet  MATH  Google Scholar 

  15. R.O. Davies: Proc. Cambridge Philos. Soc. 69, 417 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  16. T. Cochrane, C. Pinner: Proc. Amer. Math. Soc. 133, 313 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. T. Cochrane, C. Pinner: Q.J. Math. 54 no 3, 243 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. G.A. Edgar, C. Miller: Proc. Amer. Math. Soc. 131 no. 4, 1121

    Google Scholar 

  19. C. Fefferman: Ann. of Math. 94, 330 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  20. S. Konyagin: Estimates for trigonometric sums and for Gaussian sums. In: IV International Conference ‘Modern problems of number theory and its applications, Part 3 (2002) pp 86–114

    Google Scholar 

  21. S. Konyagin, I.E. Shparlinski, E. Igor: Character sums with exponential functions and their applications. In: Cambridge Tracts in Mathematics, 136 (Cambridge University Press, Cambridge 1999)

    Google Scholar 

  22. N.H. Katz, T. Tao: J.Anal. Math. 87, 231 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. N.H. Katz, T. Tao: New York J. Math. 7, 149 (2001)

    MathSciNet  MATH  Google Scholar 

  24. J. Solymosi: Preprint

    Google Scholar 

  25. I.E. Shparlinski: Period. Math. Hungar. 46 no 2, 215 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  26. E.M. Stein: Some problems in harmonic analysis. In: Harmonic analysis in Euclidean spaces. Proc. Sympos. Pure Math. (Williams Coll., Williamstown, Mass. 1978), Part 1, pp 2–20

    Google Scholar 

  27. T. Tao: Geom. Funct. Anal. 13 no 6, 1359 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  28. N.Th. Varopoulos, L. Saloff-Coste, T. Coulhon: Analysis and geometry on groups (Cambridge University Press, Cambridge 1992)

    Google Scholar 

  29. T. Wolff: Rev. Mat. Iberoamericana 11 no 3, 651 (1995)

    MATH  MathSciNet  Google Scholar 

  30. T. Wolff: Maximal averages and packing of one-dimensional sets. In: Proceedings of International Congress of Mathematicians, vol II (Berlin 1998) pp 755–761

    MATH  MathSciNet  Google Scholar 

  31. T. Wolff: Recent work connected with the Kakeya problem. In: Prospects in Mathematics (Princeton, NJ, 1996) pp 129–162

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Advanced Study, School of Mathematics, Princeton, NJ, 08540, USA

    J. Bourgain

Authors
  1. J. Bourgain
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Michael Benedicks  & Stanislav Smirnov  & 

  2. Department of Mathematics, Yale University, 10 Hillhouse Ave, P.O. Box 208283, New Haven, CT, 06520-8283, USA

    Peter W. Jones

  3. Section de Mathématiques, Université de Genève, 2-4, rue du Lièvre, 1211, Genève 4, Switzerland

    Stanislav Smirnov

  4. Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    Björn Winckler

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© 2005 Springer-Verlag Berlin Heidelberg

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Bourgain, J. (2005). New Encounters in Combinatorial Number Theory: From the Kakeya Problem to Cryptography. In: Benedicks, M., Jones, P.W., Smirnov, S., Winckler, B. (eds) Perspectives in Analysis. Mathematical Physics Studies, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30434-7_2

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