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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

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Table of Contents

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Front/Back Matter

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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