Publisher's Synopsis
This book provides an introduction to four central problemsin analytic number theory. These are(1) the problem of estimating the number of integerpointsin planar domains(2) the problem of the distribution of prime numbers in thesequence of all natural numbers and in arithmeticprogressions(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 ofanalytic number theory: complex integration,I.M.Vinogradov's method of trigonometric sums, and thecircle method of G.H.Hardy, J.E.Littlewood, and S.Ramanujan.There are numerous exercises at the end of each chapter.These exercises either refine the theorems proved in thetext, or lead to new ideas in number theory. The author alsoincludes a section of hints for the solution of theexercises.The mathematical prerequisites for this volume areundergraduate courses in number theroy, mathematicalanalysis, and complex variables. The book would be anexcellent text for a one or two semester course in analyticnumber theory for advanced undergraduates or graduatestudents.
