A conditional result on Goldbach numbers in short intervals

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1. [1] H. Davenport, Multiplicative Number Theory, 2nd ed., Springer, 1980. Zbl0453.10002
2. [2] J. B. Friedlander and D. A. Goldston, Some singular series averages and the distribution of Goldbach numbers in short intervals, Illinois J. Math. 39 (1995), 158-180. Zbl0814.11048
3. [3] D. A. Goldston, Linnik's theorem on Goldbach numbers in short intervals, Glasgow Math. J. 32 (1990), 285-297. Zbl0719.11065
4. [4] D. A. Goldston and H. L. Montgomery, Pair correlation of zeros and primes in short intervals, in: Analytic Number Theory and Dioph. Probl., A. C. Adolphson et al. (eds.), Birkhäuser, 1987, 183-203. Zbl0629.10032
5. [5] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, 1990. Zbl0020.29201
6. [6] D. R. Heath-Brown, Gaps between primes, and the pair correlation of zeros of the zeta-function, Acta Arith. 41 (1982), 85-99. Zbl0414.10044
7. [7] L. K. Hua, Introduction to Number Theory, Springer, 1982. 
8. [8] I. Kátai, A remark on a paper of Yu. V. Linnik, Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 17 (1967), 99-100 (in Hungarian). 
9. [9] A. Languasco and A. Perelli, On Linnik's theorem on Goldbach numbers in short intervals and related problems, Ann. Inst. Fourier (Grenoble) 44 (1994), 307-322. Zbl0799.11040
10. [10] A. Languasco and A. Perelli, A pair correlation hypothesis and the exceptional set in Goldbach's problem, Mathematika 43 (1996), 349-361. Zbl0884.11042
11. [11] Yu. V. Linnik, Some conditional theorems concerning the binary Goldbach problem, Izv. Akad. Nauk SSSR Ser. Mat. 16 (1952), 503-520 (in Russian). Zbl0049.03104
12. [12] H. L. Montgomery, Topics in Multiplicative Number Theory, Lecture Notes in Math. 227, Springer, 1971. Zbl0216.03501
13. [13] H. L. Montgomery, The pair correlation of zeros of the zeta function, in: Proc. Sympos. Pure Math. 24, Amer. Math. Soc., 1973, 181-193. Zbl0268.10023
14. [14] H. L. Montgomery and R. C. Vaughan, The exceptional set in Goldbach's problem, Acta Arith. 27 (1975), 353-370. Zbl0301.10043
15. [15] E. C. Titchmarsh, The Theory of Riemann Zeta-Function, 2nd ed., Oxford Univ. Press, 1986. Zbl0601.10026

1. A. Languasco, A singular series average and Goldbach numbers in short intervals