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Additive Number Theory: Inverse Problems and the Geometry of Sumsets

Melvyn B. Nathanson (Autor)

Buch | Hardcover

295 Seiten

1996 | 1996 ed.
Springer-Verlag New York Inc.
978-0-387-94655-9 (ISBN)

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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.

Reihe/Serie	Graduate Texts in Mathematics ; 165
Zusatzinfo	XIV, 295 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	0-387-94655-1 / 0387946551
ISBN-13	978-0-387-94655-9 / 9780387946559
Zustand	Neuware