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 Erdős, Szemerédi, 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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Dedicated to the memory of Paul Erdős
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© 1998 Springer Science+Business Media Dordrecht
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Ford, K. (1998). Sums and Products from a Finite Set of Real Numbers. In: Alladi, K., Elliott, P.D.T.A., Granville, A., Tenebaum, G. (eds) Analytic and Elementary Number Theory. Developments in Mathematics, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4507-8_7
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DOI: https://doi.org/10.1007/978-1-4757-4507-8_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5058-1
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