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正版现货 加性数论 经典基 [美] 纳森 著 北京世图科技
9787510044090
￥ 40.9 全新
库存5件
北京东城
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作者佚名
出版社世界图书出版公司
ISBN9787510044090
出版时间2015-01
装帧平装
货号669778958263
上书时间2024-05-01
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名称：加性数论 经典基 [美] 纳森 著 北京世图科技
作者：佚名
品相：全新
出版时间：2015-01
装订：平装
ISBN：9787510044090
出版社：世界图书出版公司
商品描述：
定价：49.00元 《加性数论（经典基）》分为上下2卷。堆垒数论讨论的是很经典的直接问题。在这个问题中，首先假定有一个自然数集合a和大于等于2的整数h，定义的和集ha是由所有的h和a中元素乘积的和组成，试图描述和集ha的结构；相反地，在逆问题中，从和集ha开始，去寻找这样的一个集合a。近年来，有关整数有限集的逆问题方面取得了显著进展。特别地，freiman， kneser， pl＆uuml;nnecke， vosper以及一些其他的学者在这方面做出了突出的贡献。本书中包括了这些结果，并且用freiman定理的ruzsa证明将本书的内容推向了高潮。 preface notation and conventior i waring's problem 1 sums of polygor 1.1 polygonal number 1.2 lagrange's theorem 1.3 quadratic forms 1.4 ternary quadratic forms 1.5 sums of three squares 1.6 thin sets of squares 1.7 the polygonal number theorem 1.8 notes 1.9 exercises 2 waring's problem for cubes 2.1 sums of cubes 2.2 the wieferich-kempner theorem 2.3 linnik's theorem 2.4 sums of two cubes 2.5 notes .2.6 exercises 3 the hilbert-waring theorem 3.1 polynomial identities and a conjecture of hurwitz 3.2 hermite polynomials and hilbert's identity 3.3 a proof by induction 3.4 notes 3.5 exercises 4 weyl's inequality 4.1 tools 4.2 difference operator 4.3 easier waring's problem 4.4 fractional parts 4.5 weyl's inequality and hua's lemma 4.6 notes 4.7 exercises 5 the hardy-littlewood asymptotic formula 5.1 the circle method 5.2 waring's problem for k = 1 5.3 the hardy-littlewood decomposition 5.4 the minor arcs 5.5 the major arcs 5.6 the singular integral 5.7 the singular series 5.8 conclusion 5.9 notes 5.10 exercises ii the goldbach conjecture 6 elementary estimates for primes 6.1 euclid's theorem 6.2 chebyshev's theorem 6.3 merter's theorems 6.4 brun's method and twin primes 6.5 notes 6.6 exercises 7 the shnirel'man-goldbach theorem 7.1 the goldbach conjecture 7.2 the selberg sieve 7.3 applicatior of the sieve 7.4 shnirel'man derity 7.5 the shnirel'man-goldbach theorem 7.6 romanov's theorem 7.7 covering congruences 7.8 notes 7.9 exercises 8 sums of three primes 8.1 vinogradov's theorem 8.2 the singular series 8.3 decomposition into major and minor arcs 8.4 the integral over the major arcs 8.5 an exponential sum over primes 8.6 proof of the asymptotic formula 8.7 notes 8.8 exercise 9 the linear sieve 9.1 a general sieve 9.2 cortruction of a combinatorial sieve 9.3 approximatior 9.4 the jurkat-richert theorem 9.5 differential-difference equatior 9.6 notes 9.7 exercises 10 chen's theorem 10.1 primes and almost primes 10.2 weights 10.3 prolegomena to sieving 10.4 a lower bound for
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