Extremal Properties of Product Sets

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Abstract

We find the nearly optimal size of a set A ⊂ [N]:= {1,..,N} so that the product set AA satisfies either (i) |AA| ~ |A| 2 /2 or (ii) |AA| ~ |[N][N]|. This settles problems recently posed in a paper of J. Cilleruelo, D. S. Ramana and O. Ramaré.

Original languageEnglish (US)
Pages (from-to)220-226
Number of pages7
JournalProceedings of the Steklov Institute of Mathematics
Volume303
Issue number1
DOIs
StatePublished - Nov 1 2018

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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