Few sums, many products

Gy Elekes, I. Ruzsa

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Let A be a set of n real numbers such that the number of distinct twofold sums is αn. We show that the number of twofold products is ≧ cn2/(α4 log n), and the number of quotients is ≧ cn2/min (α6, α 4 log n) with some absolute constant c. For bounded α this gives the correct order of magnitude for the quotients. For sums we think that the correct order is n2/(log n)a with some a <1, perhaps with 2 log 2 - 1, as a result of Pomerance and Sárközy suggests. We also give more general inequalities for sums, products and quotients formed with different sets. The proofs use geometric tools, mainly the Szemerédi-Trotter inequality.

Original language English 301-308 8 Studia Scientiarum Mathematicarum Hungarica 40 3 https://doi.org/10.1556/SScMath.40.2003.3.4 Published - 2003

Quotient
Distinct

• Product set
• Sumset

ASJC Scopus subject areas

• Mathematics(all)

Cite this

Few sums, many products. / Elekes, Gy; Ruzsa, I.

In: Studia Scientiarum Mathematicarum Hungarica, Vol. 40, No. 3, 2003, p. 301-308.

Research output: Contribution to journalArticle

Elekes, Gy ; Ruzsa, I. / Few sums, many products. In: Studia Scientiarum Mathematicarum Hungarica. 2003 ; Vol. 40, No. 3. pp. 301-308.
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