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  • © 1996

Additive Number Theory: Inverse Problems and the Geometry of Sumsets

Part of the book series: Graduate Texts in Mathematics (GTM, volume 165)

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About this book

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, Pl√ľnnecke, 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.

Keywords

  • CON_D035

Authors and Affiliations

  • Dept. Mathematics, City University of New York Lehman College, Bronx, USA

    Melvyn B. Nathanson

Bibliographic Information

  • Book Title: Additive Number Theory: Inverse Problems and the Geometry of Sumsets

  • Authors: Melvyn B. Nathanson

  • Series Title: Graduate Texts in Mathematics

  • Publisher: Springer New York, NY

  • Copyright Information: Springer-Verlag New York 1996

  • Hardcover ISBN: 978-0-387-94655-9Published: 22 August 1996

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XIV, 295

  • Topics: Number Theory, Geometry

Buying options

Hardcover Book USD 109.99
Price excludes VAT (USA)