On the exceptional set of Goldbach numbers in a short interval

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1. [1] P. X. Gallagher, A large sieve density estimate near σ = 1, Invent. Math. 11 (1970), 329-339. Zbl0219.10048
2. [2] D. R. Heath-Brown and H. Iwaniec, On the difference between consecutive primes, Invent. Math. 55 (1979), 49-69. Zbl0424.10028
3. [3] L. K. Hua, Some results in the additive prime number theory, Quart. J. Math. Oxford 9 (1938), 68-80. Zbl0018.29404
4. [4] M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170. Zbl0241.10026
5. [5] M. N. Huxley, Large values of Dirichlet polynomials III, Acta Arith. 26 (1975), 435-444. Zbl0268.10026
6. [6] H. Iwaniec, A new form of the error term in the linear sieve, Acta Arith. 37 (1980), 307-320. Zbl0444.10038
7. [7] C. H. Jia, Three primes theorem in a short interval (III), Sci. China Ser. A 34 (1991), 1039-1056. Zbl0743.11055
8. [8] C. H. Jia, Three primes theorem in a short interval (V), Acta Math. Sinica (N.S.) 7 (1991), 135-170. Zbl0735.11051
9. [9] C. H. Jia, On Pjateckiĭ-Šapiro prime number theorem (II), Sci. China Ser. A 36 (1993), 913-926. Zbl0790.11063
10. [10] C. H. Jia, Goldbach numbers in short interval, Sci. China Ser. A 24 (1994), 1233-1259 (in Chinese); I. Sci. China Ser. A 38 (1995), 385-406; II. Sci. China Ser. A 38 (1995), 513-523. 
11. [11] C. H. Jia, On the difference between consecutive primes, Sci. China Ser. A 38 (1995), 1163-1186. Zbl0844.11057
12. [12] H. Li, On the Goldbach numbers in short interval, Sci. China Ser. A, to appear. 
13. [13] H. Mikawa, On the exceptional set in Goldbach's problem, Tsukuba J. Math. 16 (1992), 513-543. Zbl0778.11054
14. [14] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, Berlin, 1971. Zbl0216.03501
15. [15] Chengdong Pan and Chengbiao Pan, Goldbach Conjecture, Science Press, Beijing, 1981 (in Chinese). 
16. [16] Chengdong Pan and Chengbiao Pan, The Basis of Analytic Number Theory, Science Press, Beijing, 1991 (in Chinese). 
17. [17] A. Perelli and J. Pintz, On the exceptional set for Goldbach's problem in short intervals, J. London Math. Soc. (2) 47 (1993), 41-49. Zbl0806.11042
18. [18] K. Ramachandra, On the number of Goldbach numbers in small intervals, J. Indian Math. Soc. 37 (1973), 157-170. Zbl0326.10041
19. [19] B. Saffari and R. C. Vaughan, On the fractional parts of x/n and related sequences II, Ann. Inst. Fourier (Grenoble) 27 (1977), 1-30. Zbl0379.10023
20. [20] P. Shiu, A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Angew. Math. 313 (1980), 161-170. Zbl0412.10030
21. [21] N. Watt, Short intervals almost all containing primes, Acta Arith. 72 (1995), 131-167. Zbl0832.11030

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