Primes in Arithmetic Progressions to Large Moduli I: Fixed Residue Classes

James Maynard, University of Oxford, United Kingdom.

• Chapters1. Introduction2. Comparison with previous results3. Outline4. Corollaries 1.2, 1.3, and 1.4 from Theorem 1.15. Paper structure6. Notation7. Sieve decomposition8. Type II estimates9. Estimates for numbers with 4, 5, or 6 prime factors10. Sieve asymptotics11. Estimates for numbers with 3 prime factors12. Small factor Type II estimate13. Preparatory lemmas14. Dispersion estimates15. 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 preparations20. Triple divisor function estimates