Additive Number Theory The Classical Bases

• 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.

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)