Multiplicative Number Theory II
Primes and Sieves
Series: Cambridge Studies in Advanced Mathematics; 218;
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Product details:
- Publisher Cambridge University Press
- Date of Publication 30 November 2025
- ISBN 9781009445054
- Binding Hardback
- No. of pages473 pages
- Language English 700
Categories
Short description:
Like its celebrated companion, this long-anticipated book will prove essential reading for analytic number theorists.
MoreLong 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.
'This very readable volume, by two great expositors, will provide the student with a thorough grounding in the applications of sieves in multiplicative number theory. The exercises are a real bonus, encouraging the reader to explore in many further directions.' Roger Heath-Brown OBE FRS, University of Oxford
Table of 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.
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