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Analytic Number Theory
About this Title
Henryk Iwaniec, Rutgers University, Piscataway, NJ and Emmanuel Kowalski, Université Bordeaux I, Talence, France
Publication: Colloquium Publications
Publication Year:
2004; Volume 53
ISBNs: 978-0-8218-3633-0 (print); 978-1-4704-3198-3 (online)
DOI: https://doi.org/10.1090/coll/053
MathSciNet review: MR2061214
MSC: Primary 11-02; Secondary 11Fxx, 11Lxx, 11Mxx, 11Nxx
Table of Contents
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Front/Back Matter
Chapters
- Introduction
- Chapter 1. Arithmetic functions
- Chapter 2. Elementary theory of prime numbers
- Chapter 3. Characters
- Chapter 4. Summation formulas
- Chapter 5. Classical analytic theory of $L$-functions
- Chapter 6. Elementary sieve methods
- Chapter 7. Bilinear forms and the large sieve
- Chapter 8. Exponential sums
- Chapter 9. The Dirichlet polynomials
- Chapter 10. Zero-density estimates
- Chapter 11. Sums over finite fields
- Chapter 12. Character sums
- Chapter 13. Sums over primes
- Chapter 14. Holomorphic modular forms
- Chapter 15. Spectral theory of automorphic forms
- Chapter 16. Sums of Kloosterman sums
- Chapter 17. Primes in arithmetic progressions
- Chapter 18. The least prime in an arithmetic progression
- Chapter 19. The Goldbach problem
- Chapter 20. The circle method
- Chapter 21. Equidistribution
- Chapter 22. Imaginary quadratic fields
- Chapter 23. Effective bounds for the class number
- Chapter 24. The critical zeros of the Riemann zeta function
- Chapter 25. The spacing of zeros of the Riemann zeta-function
- Chapter 26. Central values of $L$-functions