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加性数论 经典基PDF|Epub|txt|kindle电子书版本网盘下载
- （美）纳森著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510044090
- 出版时间：2012
- 标注页数：344页
- 文件大小：6MB
- 文件页数：360页
- 主题词：堆垒数论－研究－英文
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图书目录
Ⅰ Waring's problem3
1 Sums ofpolygons3
1.1 Polygonal numbers4
1.2 Lagrange's theorem5
1.3 Quadratic forms7
1.4 Ternary quadratic forms12
1.5 Sums ofthree squares17
1.6 Thin sets of squares24
1.7 The polygonal numbertheorem27
1.8 Notes33
1.9 Exercises34
2 Waring'sproblem forcubes37
2.1 Sums ofcubes37
2.2 The Wieferich-Kempnertheorem38
2.3 Linnik's theorem44
2.4 Sums oftwo cubes49
2.5 Notes71
2.6 Exercises72
3 The Hilbert-Waring theorem75
3.1 Polynomial identities and a conjecture ofHurwitz75
3.2 HermitepolynomialsandHilbert's identity77
3.3 A proofby induction86
3.4 Notes94
3.5 Exercises94
4 Weyl's inequality97
4.1 Tools97
4.2 Difference operators99
4.3 Easier Waring's problem102
4.4 Fractional parts103
4.5 Weyl's inequality and Hua's lemma111
4.6 Notes118
4.7 Exercises118
5 The Hardy-Littlewood asymptotic formula121
5.1 The circle method121
5.2 Waring's problem for k-l124
5.3 The Hardy-Littlewood decomposition125
5.4 The minor arcs127
5.5 The major arcs129
5.6 The singular integral133
5.7 The singular series137
5.8 Conclusion146
5.9 Notes147
5.10 Exercises147
Ⅱ The Goldbach conjecture151
6 Elementary estimates for primes151
6.1 Euclid's theorem151
6.2 Chebyshev's theorem153
6.3 Mertens's theorems158
6.4 Brun's method and twin primes167
6.5 Notes173
6.6 Exercises174
7 The Shnlrel?man-Goldbach theorem177
7.1 The Goldbach conjecture177
7.2 The Selberg sieve178
7.3 Applications ofthe sieve186
7.4 Shnirel'man density191
7.5 The Shnirel'man-Goldbach theorem195
7.6 Romanov's theorem199
7.7 Covering congruences204
7.8 Notes208
7.9 Exercises208
8 Sums of three primes211
8.1 Vinogradov's theorem211
8.2 The singular series212
8.3 Decomposition into major and minor arcs213
8.4 The integral over the major arcs215
8.5 An exponential sum over primes220
8.6 Proof of the asymptotic formula227
8.7 Notes230
8.8 Exercise230
9 The linear sieve231
9.1 A general sieve231
9.2 Construction of a combinatorial sieve238
9.3 Approximations244
9.4 The Jurkat-Richert theorem251
9.5 Differential-difference equations259
9.6 Nores267
9.7 Exercises267
10 Chen's theorem271
10.1 Primes and almost primes271
10.2 Weights272
10.3 Prolegomena to sieving275
10.4 A lower bound for S(A,P,z)279
10.5 An upper bound for S(Aq,P,z)281
10.6 An upper bound for S(B,P,y)286
10.7 A bilinear form inequality292
10.8 Conclusion297
10.9 Notes298
Ⅲ Appendix301
Arithmetic funetions301
A.1 The ring of arithtmetic functions301
A.2 Sums and integrals303
A.3 Multiplicative functions308
A.4 The divisor function310
A.5 THe Euler ？－function314
A.6 The M？bius function317
A.7 Ramanujan sums320
A.8 Infinite products323
A.9 Nores327
A.10 Exercises327
Bibliography331
Index341