Multiplicative Number Theory II

Primes and Sieves
Erscheinungsjahr 2025
ISBN: 978-1-009-44505-4
Verlag: Cambridge University Press

Buch, Englisch, Band 218, 473 Seiten

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Montgomery, Hugh L

Vaughan, Robert C

Inhaltsverzeichnis

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.

Über Autor(innen)

Montgomery, Hugh L
Hugh L. Montgomery is Professor Emeritus in the Department of Mathematics at the University of Michigan, Ann Arbor.

Vaughan, Robert C
Robert C. Vaughan is Professor of Mathematics at Pennsylvania State University.