The distribution of prime numbers: large sieves and zero-density theorems,
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford :
Clarendon Press,
1972
Oxford, 1972 |
| Series: | Oxford mathematical monographs
Oxford mathematical monographs |
| Subjects: |
Table of Contents:
- pt. I. Introductory results. Arithmetical functions
- Some sum functions
- Characters
- Pólya's theorem
- Dirichlet series
- Schinzel's hypothesis
- The large sieve
- The upper-bound sieve
- Franel's theorem
- pt. II. The prime-number theorem. A modular relation
- The functional equations
- Hadamard's product formula
- Zeros of [xi](s)
- Zeros of [xi](s, [chi])
- The exceptional zero
- The prime-number theorem
- The prime-number theorem for an arithmetic progression
- pt. III. The necessary tools. A survey of sieves
- The hybrid sieve
- An approximate functional equation (I)
- An approximate functional equation (II)
- Fourth powers of L-functions
- pt. IV. Zeros and prime numbers. Ingham's theorem
- Bombierie's theorem
- I.M. Vinogradov's estimate
- I.M. Vinogradov's three-primes theorem
- Halász's method
- Gaps between prime numbers