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| 读者对象：数学专业的研究生和相关专业的科研人员。 |
| 《加性数论：经典基》 preface notation and conventions i waring's problem 1 sums of polygons 1.1 polygonal numbers 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 operators 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 mertens'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 applications of the sieve 7.4 shnirel'man density 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 construction of a combinatorial sieve 9.3 approximations 9.4 the jurkat-richert theorem 9.5 differential-difference equations 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 s(a, p, z) 10.5 an upper bound for s(aq, p, z) 10.6 an upper bound for s(b, p, y) 10.7 a bilinear form inequality 10.8 conclusion 10.9 notes 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.5 the euler φ-function a.6 the mobius function a.7 ramanujan sums a.8 infinite products a.9 notes a.10 exercises bibliography index |
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