Basic Analytic Number Theory

This book provides an introduction to four central problems in analytic number theory. These are (1) the problem of estimating the number of integerpoints in planar domains (2) the problem of the distribution of prime numbers in the sequence of all natural numbers and in arithmetic progressions (3) Goldbach's problem on sums of primes, and (4) Waring's problem on sums of k-th powers. To solve these problems, one uses the fundamental methods of analytic number theory: complex integration, I.M.Vinogradov's method of trigonometric sums, and the circle method of G.H.Hardy, J.E.Littlewood, and…