Multiplicative Number Theory II : Primes and Sieves (Cambridge Studies in Advanced Mathematics)

Montgomery, Hugh L./ Vaughan, Robert C.

Cambridge University Press（2025/10発売）

• 製本 Hardcover:ハードカバー版／ページ数 473 p.
• 言語 ENG
• 商品コード 9781009445054

Full Description

This long-anticipated work shares the aims of its celebrated companion: namely, to provide an introduction for students and a reference for researchers to the techniques, results, and terminology of multiplicative number theory. This volume builds on the earlier one (which served as an introduction to basic, classical results) and focuses on sieve methods. This area has witnessed a number of major advances in recent years, e.g. gaps between primes, large values of Dirichlet polynomials and zero density estimates, all of which feature here. Despite the fact that the book can serve as an entry to contemporary mathematics, it remains largely self-contained, with appendices containing background or material more advanced than undergraduate mathematics. Again, exercises, of which there is a profusion, illustrate the theory or indicate ways in which it can be developed. Each chapter ends with a thorough set of references, which will be essential for all analytic number theorists.

Contents

16. Exponential sums I: Van der Corput's method; 17. Estimates for sums over primes; 18. Additive prime number theory; 19. The large sieve; 20. Primes in arithmetic progressions: III; 21. Sieves II; 22. Bounded gaps between primes; E. Topics in harmonic analysis II; F. Uniform distribution; G. Bounds for bilinear forms; H. Linear programming; Errata for Volume I; Name index; Subject index.