On the least almost‐prime in an arithmetic progression
Abstract
Abstract For all sufficiently large , in any arithmetic progression in which and are relatively prime there exists a positive integer with at most two prime factors (counted with multiplicity) which is asymptotically less than . The proof uses the weighted sieve of Greaves–Halberstam–Richert with bilinear remainder terms and Selberg's sieve.
Fields of Study & Subjects
Analytic Number Theory Research
Limits and Structures in Graph Theory
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 2
- Publication date
- 5 March 2026
- Language
- EN