Multiplicative Number Theory II

Primes and Sieves

AvHugh L. Montgomery,Robert C. Vaughan

Inbunden, Engelska, 2026

Del 218 i serien Cambridge Studies in Advanced Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2026-04-09
Mått:234 x 29 x 160 mm
Vikt:880 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:476
Förlag:Cambridge University Press
ISBN:9781009445054

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Mer om författaren

Hugh L. Montgomery is Professor Emeritus in the Department of Mathematics at the University of Michigan, Ann Arbor. Robert C. Vaughan, FRS, was formerly Professor of Pure Mathematics at Imperial College London, and is currently Professor of Mathematics in the Department of Mathematics at Pennsylvania State University, University Park.

Recensioner i media

'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

Innehållsförteckning

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 of fixed dimension and applications; 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.