Additive Number Theory The Classical Bases

Released on by Melvyn B. Nathanson
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  • Additive Number Theory The Classical Bases Book Detail

  • Author : Melvyn B. Nathanson
  • Release Date : 1996-06-25
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 362
  • ISBN 13 : 9780387946566
  • File Size : 14,14 MB
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Additive Number Theory The Classical Bases by Melvyn B. Nathanson PDF Summary

Book Description: [Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.

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Additive Number Theory The Classical Bases

Additive Number Theory The Classical Bases

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[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly

Additive Number Theory The Classical Bases

Additive Number Theory The Classical Bases

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[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly

Additive Number Theory

Additive Number Theory

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This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory

Elementary Methods in Number Theory

Elementary Methods in Number Theory

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This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the dis