The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
Chapters
1. Introduction
2. Comparison with previous results
3. Outline
4. Corollaries 1.2, 1.3, and 1.4 from Theorem 1.1
5. Paper structure
6. Notation
7. Sieve decomposition
8. Type II estimates
9. Estimates for numbers with 4, 5, or 6 prime factors
10. Sieve asymptotics
11. Estimates for numbers with 3 prime factors
12. Small factor Type II estimate
13. Preparatory lemmas
14. Dispersion estimates
15. Fouvry-style estimates near $x^{1/7}$
16. Small divisor estimates near $x^{1/21}$
17. Zhang-style estimates near $x^{1/2}$
18. Bombieri-Friedlander-Iwaniec-style estimates near $x^{1/5}$
19. Smoothing preparations
20. Triple divisor function estimates
James Maynard, University of Oxford, United Kingdom.
