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Liu, Jianya; Liu, Ming-Chit; Wang, Tianze

On the almost Goldbach problem of Linnik. (English) Zbl 0979.11051

J. Théor. Nombres Bordx. 11, No. 1, 133-147 (1999).
In 1953 Yu. V. Linnik [Mat. Sb., Nov. Ser. 32 (74), 3-60 (1953; Zbl 0051.03402)] showed that every large even integer can be written as a sum of two odd primes and a bounded number of powers of 2. Assuming the generalized Riemann hypothesis, the authors show that, for \(k\geq 200\), every even \(N\geq N_k\) can be written as a sum of two odd primes and at most \(k\) powers of 2. They follow the original argument of Linnik, combined with a careful treatment of the numerical constant.
Reviewer: Dieter Wolke (Freiburg i.Br.)

Cited in 1 Review
Cited in 9 Documents

MSC:

11P32 Goldbach-type theorems; other additive questions involving primes

Keywords:

almost Goldbach problem; generalized Riemann hypothesis

Citations:

Zbl 0051.03402
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\textit{J. Liu} et al., J. Théor. Nombres Bordx. 11, No. 1, 133--147 (1999; Zbl 0979.11051)
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References:

[1] Chen, J.R., On Goldbach’s problem and the sieve methods. Sci. Sin., 21 (1978), 701-739. · Zbl 0399.10046
[2] Davenport, H., Multiplicative Number Theory. 2nd ed., Springer, 1980. · Zbl 0453.10002
[3] Gallagher, P.X., Primes and powers of 2. Invent. Math.29(1975), 125-142. · Zbl 0305.10044
[4] Hardy, G.H. and Littlewood, J.E., Some problems of “patitio numerorum” V: A further contribution to the study of Goldbach’s problem. Proc. London Math. Soc. (2) 22 (1923), 45-56. · JFM 49.0127.03
[5] Halberstam, H. and Richert, H.-E., Sieve Methods, Academic Press, 1974. · Zbl 0298.10026
[6] Kaczorowski, J., Perelli, A. and Pintz, J., A note on the exceptional set for Goldbach’s problem in short intervals. Mh. Math.116 (1993), 275-282; corrigendum 119 (1995), 215-216. · Zbl 0836.11034
[7] Linnik, Yu. V., Prime numbers and powers of two. Trudy Mat. Inst. Steklov38 (1951), 151-169. · Zbl 0049.31402
[8] Linnik, Yu.V., Addition of prime numbers and powers of one and the same number. Mat. Sb.(N. S.) 32 (1953), 3-60. · Zbl 0051.03402
[9] Liu, J.Y., Liu, M.C., and Wang, T.Z., The number of powers of 2 in a representation of large even integers (I). Sci. China Ser. A 41 (1998), 386-398. · Zbl 1029.11049
[10] Liu, J.Y., Liu, M.C., and Wang, T.Z., The number of powers of 2 in a representation of large even integers (II). Sci. China Ser. A. 41 (1998), 1255-1271. · Zbl 0924.11086
[11] Languasco, A. and Perelli, A., A pair correlation hypothesis and the exceptional set in Goldbach’s problem. Mathematika43 (1996), 349-361. · Zbl 0884.11042
[12] Prachar, K., Primzahlverteilung. Springer, 1957. · Zbl 0080.25901
[13] Romanoff, N.P., Über einige Sätze der additiven Zahlentheorie. Math. Ann.109 (1934), 668-678. · JFM 60.0131.03
[14] Rosser, J.B. and Schoenfeld, L., Approximate formulas for some functions of prime numbers. Illinois J. Math.6 (1962), 64-94. · Zbl 0122.05001
[15] Vinogradov, A.I., On an “almost binary” problem. Izv. Akad. Nauk. SSSR Ser. Mat.20 (1956), 713-750. · Zbl 0072.27001
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