Sums and products from a finite set of real numbers

Kevin Ford

doi:10.1023/a:1009709908223

Sums and products from a finite set of real numbers

Kevin Ford

Research output: Contribution to journal › Article › peer-review

Abstract

If A is a finite set of positive integers, let E_h, (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 f_h(k), the minimum of |E_h,(A)| taken over all A with |A| = k. Upper and lower bounds for f_h, (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 language	English (US)
Pages (from-to)	59-66
Number of pages	8
Journal	Ramanujan Journal
Volume	2
Issue number	1-2
DOIs	https://doi.org/10.1023/a:1009709908223
State	Published - 1998
Externally published	Yes

Keywords

Products
Sequences
Sums

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1023/a:1009709908223

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abstract = "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, Szemer{\'e}di, and Nathanson. Moreover, the lower bound holds when we allow A to be a finite set of arbitrary positive real numbers.",

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AB - 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.

KW - Products

KW - Sequences

KW - Sums

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ER -

Sums and products from a finite set of real numbers

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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