Oscillation theorems for primes in arithmetic progressions and for sifting functions

Abstract

Introduction 1. Primes in arithmetic progressions 2. The main theorems II.Oscillation theorems for sifting functions 3. The statements 4. Proof of Theorem B2 5. Proof of Proposition 3.1 6. Proof of Proposition 3.2 7. Proof of Theorem C: preliminaries 8. Proof of Theorem C: completion 9. Proof of Theorem Bl 10.Proof of Theorem B3 III.Oscillation theorems for primes 11.Proof of Theorem Al 12. Proof of Theorem A2 13.Proofs of Theorem A3 and Proposition 2.1 I. INTRODUCTION 1. PRIMES IN ARITHMETIC PROGRESSIONSFor x ~ 2 real, q a positive integer, and a an integer coprime to q, let 0 and ~ be defined by (1.1) O(x; q, a) = E logp = qJZq) (1 +~(x; q, a)), p~x p=amodq

Locations

• Journal of the American Mathematical Society - View - PDF