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Sequences: Volume 1
Edité par
Oxford University Press / Clarendon, 1966
ISBN 10 : 0198533268
ISBN 13 : 9780198533269
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Vendeur : killarneybooks, Inagh, CLARE, Irlande
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Hardcover. Etat : Very Good. No Jacket. 1st Edition. Hardcover, xx + 292 pages, NOT ex-library. Interior is clean, untanned, with unmarked text, free of inscriptions and stamps, firmly bound. Faint marks and some age-toning on the outer page edges. Boards show sunning along the lower edges; a bit of rubbing to the spine ends and tips of corners. Missing the dust jacket. -- This is a foundational graduate-level text in additive number theory. The book focuses on the properties of sequences of non-negative integers and the methods used to study their arithmetic structures. Core Mathematical Focus: The book is primarily concerned with distributional properties and the summation of sequences. Schnirelmann Density: The authors provide a rigorous treatment of the density of integer sequences and the conditions under which every integer can be represented as a sum of elements from a specific sequence. Essential Components: It explores "essential components" and "bases" of the natural numbers (e.g., the sequence of squares or primes). Sieve Methods: The text introduces early iterations of sieve theory, which are critical for estimating the number of elements in a sequence that satisfy certain arithmetic conditions (like being prime). Probabilistic Number Theory: A significant portion (Chapter 3) is dedicated to the probabilistic methods of Erdos and others, showing that "almost all" sequences of a certain type possess specific properties. Key Chapters: Addition of Sequences: Density Theorem (covers the Schnirelmann and Mann theorems); Addition of Sequences: Basis Theorems (discusses the order of a basis and the Waring's Problem context); Probabilistic Methods (focuses on the existence of sequences with prescribed properties); Sieve Methods (introduction to the Brun Sieve and its applications); Primitive Sequences and Density Questions (analysis of sequences where no element divides another). Authorship Note: Heini Halberstam: A renowned mathematician best known for the Elliott-Halberstam conjecture. K.F. Roth: A Fields Medalist (1958) famous for his work on Diophantine approximation (Roth's Theorem). N° de réf. du vendeur 012301
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