On sum-sets and product-sets of complex numbers

József Solymosi[1]

  • [1] Department of Mathematics, University of British Columbia 1984 Mathematics Road, Vancouver, Colombie-Britannique, Canada V6T 1Z2

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 3, page 921-924
  • ISSN: 1246-7405

Abstract

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We give a simple argument that for any finite set of complex numbers A , the size of the the sum-set, A + A , or the product-set, A · A , is always large.

How to cite

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Solymosi, József. "On sum-sets and product-sets of complex numbers." Journal de Théorie des Nombres de Bordeaux 17.3 (2005): 921-924. <http://eudml.org/doc/249441>.

@article{Solymosi2005,
abstract = {We give a simple argument that for any finite set of complex numbers $A$, the size of the the sum-set, $A+A$, or the product-set, $A\cdot A$, is always large.},
affiliation = {Department of Mathematics, University of British Columbia 1984 Mathematics Road, Vancouver, Colombie-Britannique, Canada V6T 1Z2},
author = {Solymosi, József},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {sum-sets; product-sets},
language = {eng},
number = {3},
pages = {921-924},
publisher = {Université Bordeaux 1},
title = {On sum-sets and product-sets of complex numbers},
url = {http://eudml.org/doc/249441},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Solymosi, József
TI - On sum-sets and product-sets of complex numbers
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 3
SP - 921
EP - 924
AB - We give a simple argument that for any finite set of complex numbers $A$, the size of the the sum-set, $A+A$, or the product-set, $A\cdot A$, is always large.
LA - eng
KW - sum-sets; product-sets
UR - http://eudml.org/doc/249441
ER -

References

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  1. J. Bourgain,S. Konjagin, Estimates for the number of sums and products and for exponential sums over subgrups in finite fields of prime order. C. R. Acad. Sci. Paris 337 (2003), no. 2, 75–80. Zbl1041.11056MR1998834
  2. J. Bourgain, N. Katz, T. Tao, A sum-product estimate in finite fields, and applications. Geometric And Functional Analysis GAFA 14 (2004), no. 1, 27–57. Zbl1145.11306MR2053599
  3. M. Chang, A sum-product estimate in algebraic division algebras over R. Israel Journal of Mathematics (to appear). 
  4. M. Chang, Factorization in generalized arithmetic progressions and applications to the Erdős-Szemerédi sum-product problems. Geometric And Functional Analysis GAFA 13 (2003), no. 4, 720–736. Zbl1029.11006MR2006555
  5. M. Chang, Erdős-Szemerédi sum-product problem. Annals of Math. 157 (2003), 939–957. Zbl1055.11017MR1983786
  6. Gy. Elekes, On the number of sums and products. Acta Arithmetica 81 (1997), 365–367. Zbl0887.11012MR1472816
  7. P. Erdős, E. Szemerédi, On sums and products of integers. In: Studies in Pure Mathematics; To the memory of Paul Turán. P.Erdős, L.Alpár, and G.Halász, editors. Akadémiai Kiadó – Birkhauser Verlag, Budapest – Basel-Boston, Mass. 1983, 213–218. Zbl0526.10011MR820223
  8. K. Ford, Sums and products from a finite set of real numbers. Ramanujan Journal, 2 (1998), (1-2), 59–66. Zbl0908.11008MR1642873
  9. M. B. Nathanson, On sums and products of integers. Proc. Am. Math. Soc. 125 (1997), (1-2), 9–16. Zbl0869.11010MR1343715

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