Description
Book SynopsisAnalytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques.
Trade ReviewThe book is written in a very lively and nicely readable style ... contains a very well chosen and balanced material. -- EMS Newsletter The authors are active researchers with a lot of experience and deep insight, and their creative attitude makes reading particularly rewarding... It can be warmly recommended toa wide readership ..."" —
Zentralblatt MathTable of Contents
- Introduction
- Arithmetic functions
- Elementary theory of prime numbers
- Characters
- Summation formulas
- Classical analytic theory of $L$-functions
- Elementary sieve methods
- Bilinear forms and the large sieve
- Exponential sums
- The Dirichlet polynomials
- Zero-density estimates
- Sums over finite fields
- Character sums
- Sums over primes
- Holomorphic modular forms
- Spectral theory of automorphic forms
- Sums of Kloosterman sums
- Primes in arithmetic progressions
- The least prime in an arithmetic progression
- The Goldbach problem
- The circle method
- Equidistribution
- Imaginary quadratic fields
- Effective bounds for the class number
- The critical zeros of the Riemann zeta function
- The spacing of zeros of the Riemann zeta-function
- Central values of $L$-functions
- Bibliography
- Index
