Primes in arithmetic progressions on average I
Abstract
Abstract Let We show that if is close to then essentially , thereby showing that sign‐changes in the average give power‐saving cancellation past the expected . This therefore for the first time provides unconditional evidence for a deep conjecture of Montgomery and Soundararajan.
Fields of Study & Subjects
Analytic Number Theory Research
History and Theory of Mathematics
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN