On the size of fold sum and product sets of integers
Authors:
Jean Bourgain and MeiChu Chang
Journal:
J. Amer. Math. Soc. 17 (2004), 473497
MSC (1991):
Primary 05A99
Published electronically:
November 25, 2003
MathSciNet review:
2051619
Fulltext PDF Free Access
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Abstract: In this paper, we show that for all there is a positive integer such that if is an arbitrary finite set of integers, , then either or . Here (resp. ) denotes the fold sum (resp. product) of . This fact is deduced from the following harmonic analysis result obtained in the paper. For all and , there is a such that if satisfies , then the constant of (in the sense of W. Rudin) is at most .
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Additional Information
Jean Bourgain
Affiliation:
Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540
Email:
bourgain@math.ias.edu
MeiChu Chang
Affiliation:
Mathematics Department, University of California, Riverside, California 92521
Email:
mcc@math.ucr.edu
DOI:
http://dx.doi.org/10.1090/S0894034703004466
PII:
S 08940347(03)004466
Received by editor(s):
September 5, 2003
Published electronically:
November 25, 2003
Article copyright:
© Copyright 2003
American Mathematical Society
