Multiplicative Number Theory II
Primes and Sieves
Seiten
2026
Cambridge University Press (Verlag)
978-1-009-44505-4 (ISBN)
Cambridge University Press (Verlag)
978-1-009-44505-4 (ISBN)
- Noch nicht erschienen (ca. Februar 2026)
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Long anticipated, this work focuses on sieve methods and their applications to areas such as the gaps between prime numbers, large values of Dirichlet polynomials, and zero density estimates. With numerous exercises and a thorough set of references, this book will prove essential reading for analytic number theorists.
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 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.
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.
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.
| Erscheint lt. Verlag | 28.2.2026 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 1-009-44505-7 / 1009445057 |
| ISBN-13 | 978-1-009-44505-4 / 9781009445054 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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