包邮素数与群表示论

Contents Preface The Average Number of Goldbach Representations Daniel A.Goldston Liyang Yang 1. Introduction 1 2. Results 3 3. The Main Terms in the Asymptotic Expansion 3 4. Gallagher's Lemma 6 5. Bhowmik and Schlage-Puchta's Estimate 7 6. Estimates for Primes on RH 8 7. Proof of Theorems 1 and 2 9 References 10 Sieve Methods and Exponential Sums: An Interplay Between Combinatorics and Harmonic Analysis Angel V.Kumchev Introduction 13 1. A Basic Example: The Distribution of p Modulo One 15 1.1 First result.Vaughan's identity 15 1.2 Preparation for the sieve 18 1.3 A simple lower-bound sieve 22 2. An Application to Additive Number Theory: Exceptional Sets for Sums of Squares of Primes 27 2.1 A canonical application of the circle method 29 2.2 Some background on quadratic exponential sums 32 2.3 A first sieve result 35 2.4 Zhao's major-arc idea 38 2.5 A