Sums and products from a finite set of real numbers

Research output: Contribution to journalArticlepeer-review


If A is a finite set of positive integers, let Eh, (A) denote the set of h-fold sums and h-fold products of elements of A. This paper is concerned with the behavior of the function fh(k), the minimum of |Eh,(A)| taken over all A with |A| = k. Upper and lower bounds for fh, (k) are proved, improving bounds given by Erdos, Szemerédi, and Nathanson. Moreover, the lower bound holds when we allow A to be a finite set of arbitrary positive real numbers.

Original languageEnglish (US)
Pages (from-to)59-66
Number of pages8
JournalRamanujan Journal
Issue number1-2
StatePublished - 1998
Externally publishedYes


  • Products
  • Sequences
  • Sums

ASJC Scopus subject areas

  • Algebra and Number Theory


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