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Graduate Texts in Mathematics

Additive Number Theory: Inverse Problems and the Geometry of Sumsets

Authors: Nathanson, Melvyn B.

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  • ISBN 978-0-387-94655-9
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About this Textbook

Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.

Buy this book

Hardcover 65,47 €
price for Spain (gross)
  • ISBN 978-0-387-94655-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules

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Bibliographic Information

Bibliographic Information
Book Title
Additive Number Theory: Inverse Problems and the Geometry of Sumsets
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
165
Copyright
1996
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
Hardcover ISBN
978-0-387-94655-9
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIV, 296
Topics