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

James Maynard (Autor)

Buch | Softcover

132 Seiten

2025
American Mathematical Society (Verlag)
978-1-4704-7153-8 (ISBN)

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Publishing rigorous mathematical research, these memoirs compile extended studies into cohesive volumes of pure and applied mathematics. Each paper is meticulously peer-reviewed under the vigilant oversight of an expert Editorial Committee from the AMS Transactions journal, offering a valuable resource for mathematical inquiry.

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.

James Maynard, University of Oxford, United Kingdom.

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

Erscheinungsdatum	12.06.2025
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	1-4704-7153-1 / 1470471531
ISBN-13	978-1-4704-7153-8 / 9781470471538
Zustand	Neuware