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Nathanson - Additive Zahlentheorie - Klassische Grundlagen Absolvententex
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eBay-Artikelnr.:376448957242
Artikelmerkmale
- Artikelzustand
- ISBN
- 9780387946566
Über dieses Produkt
Product Identifiers
Publisher
Springer New York
ISBN-10
038794656X
ISBN-13
9780387946566
eBay Product ID (ePID)
12038294925
Product Key Features
Number of Pages
Xiv, 342 Pages
Language
English
Publication Name
Additive Number Theory : the Classical Bases
Publication Year
1996
Subject
Number Theory, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Height
0.3 in
Item Weight
53.6 Oz
Item Length
9.2 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
96-011745
Reviews
From the reviews: "This book provides a very thorough exposition of work to date on two classical problems in additive number theory ... . is aimed at students who have some background in number theory and a strong background in real analysis. A novel feature of the book, and one that makes it very easy to read, is that all the calculations are written out in full - there are no steps 'left to the reader'. ... The book also includes a large number of exercises ... ." (Allen Stenger, The Mathematical Association of America, August, 2010), From the reviews: This book provides a very thorough exposition of work to date on two classical problems in additive number theory … . is aimed at students who have some background in number theory and a strong background in real analysis. A novel feature of the book, and one that makes it very easy to read, is that all the calculations are written out in full there are no steps 'left to the reader'. … The book also includes a large number of exercises … . (Allen Stenger, The Mathematical Association of America, August, 2010), From the reviews:This book provides a very thorough exposition of work to date on two classical problems in additive number theory … . is aimed at students who have some background in number theory and a strong background in real analysis. A novel feature of the book, and one that makes it very easy to read, is that all the calculations are written out in full there are no steps 'left to the reader'. … The book also includes a large number of exercises … . (Allen Stenger, The Mathematical Association of America, August, 2010)
Dewey Edition
20
Series Volume Number
164
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
512/.72
Table Of Content
I Waring's problem.- 1 Sums of polygons.- 2 Waring's problem for cubes.- 3 The Hilbert--Waring theorem.- 4 Weyl's inequality.- 5 The Hardy--Littlewood asymptotic formula.- II The Goldbach conjecture.- 6 Elementary estimates for primes.- 7 The Shnirel'man--Goldbach theorem.- 8 Sums of three primes.- 9 The linear sieve.- 10 Chen's theorem.- III Appendix.- Arithmetic functions.- A.1 The ring of arithmetic functions.- A.2 Sums and integrals.- A.3 Multiplicative functions.- A.4 The divisor function.- A.6 The Möbius function.- A.7 Ramanujan sums.- A.8 Infinite products.- A.9 Notes.- A.10 Exercises.
Synopsis
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., [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.
LC Classification Number
QA241-247.5
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