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Inverse problem for upper asymptotic density II

from PURE MATHEMATICS

Published online by Cambridge University Press:  30 March 2017

By
Renling Jin
Edited by
Nigel J. Cutland ,
Mauro Di Nasso  and
David A. Ross
Nigel J. Cutland
Affiliation:
University of York
Mauro Di Nasso
Affiliation:
Università degli Studi, Pisa
David A. Ross
Affiliation:
University of Hawaii, Manoa
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Nonstandard Methods and Applications in Mathematics , pp. 147 - 173
Publisher: Cambridge University Press
Print publication year: 2006

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References

Yuri, Bilu, Addition of sets of integers of positive density, The Journal of Number Theory, vol. 64, (1997), no. 2, pp. 233–275.Google Scholar
Yuri, Bilu, Structure of sets with small sumset, Asterisque, vol. 258, (1999), pp. 77–108.Google Scholar
Heini, Halberstam and Klaus Friedrich, Roth, Sequences, Oxford University Press, 1966.
Pál, Hegedüs, Gábor, Piroska, and Imre Z., Ruzsa, Onthe Schnirelmann density of sumsets, Publicationes Mathematicae Debrecen, vol. 53, (1998), no. 3–4, pp. 333–345.Google Scholar
C., Ward Henson, Foundations of nonstandard analysis—a gentle introduction to nonstandard extension, Nonstandard analysis: Theory and applications (Nigel J., Cutland, C., Ward Henson, and Leif, Arkeryd, editors), Kluwer Academic Publishers, 1997.
Renling, Jin, Nonstandard methods for upper Banach density problems, The Journal of Number Theory, vol. 91, (2001), pp. 20–38.Google Scholar
Renling, Jin, Inverse problem for upper asymptotic density, The Transactions of American Mathematical Society, vol. 355, (2003), no. 1, pp. 57–78.Google Scholar
Tom, Lindstrom, An invitation to nonstandard analysis, Nonstandard analysis and its application (Nigel J., Cutland, editor), Cambridge University Press, 1988.
Melvyn B., Nathanson, Additive number theory—inverse problems and the geometry of sumsets, Springer, 1996.

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