Additive Number Theory the Classical Bases (Paperback)

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 Mobius function.- A.7 Ramanujan sums.- A.8 Infinite products.- A.9 Notes.- A.10 Exercises.