On the almost Goldbach problem of Linnik

Jianya Liu; Ming-Chit Liu; Tianze Wang

Jianya Liu ; Ming-Chit Liu ; Tianze Wang

Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 133-147

Abstract (VO)
Résumé

Under the Generalized Riemann Hypothesis, it is proved that for any $k \geq 200$ there is $N_{k} > 0$ depending on $k$ only such that every even integer $\geq N_{k}$ is a sum of two odd primes and $k$ powers of $2$ .

On démontre que sous GRH et pour $k \geq 200$ , tout entier pair assez grand est somme de deux nombres premiers impairs et de $k$ puissances de $2$ .

MR Zbl

@article{JTNB_1999__11_1_133_0,
     author = {Jianya Liu and Ming-Chit Liu and Tianze Wang},
     title = {On the almost {Goldbach} problem of {Linnik}},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {133--147},
     year = {1999},
     publisher = {Universit\'e Bordeaux I},
     volume = {11},
     number = {1},
     zbl = {0979.11051},
     mrnumber = {1730436},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1999__11_1_133_0/}
}

TY  - JOUR
AU  - Jianya Liu
AU  - Ming-Chit Liu
AU  - Tianze Wang
TI  - On the almost Goldbach problem of Linnik
JO  - Journal de théorie des nombres de Bordeaux
PY  - 1999
SP  - 133
EP  - 147
VL  - 11
IS  - 1
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/item/JTNB_1999__11_1_133_0/
LA  - en
ID  - JTNB_1999__11_1_133_0
ER  -

%0 Journal Article
%A Jianya Liu
%A Ming-Chit Liu
%A Tianze Wang
%T On the almost Goldbach problem of Linnik
%J Journal de théorie des nombres de Bordeaux
%D 1999
%P 133-147
%V 11
%N 1
%I Université Bordeaux I
%U https://jtnb.centre-mersenne.org/item/JTNB_1999__11_1_133_0/
%G en
%F JTNB_1999__11_1_133_0

Jianya Liu; Ming-Chit Liu; Tianze Wang. On the almost Goldbach problem of Linnik. Journal de théorie des nombres de Bordeaux, Tome 11 (1999) no. 1, pp. 133-147. https://jtnb.centre-mersenne.org/item/JTNB_1999__11_1_133_0/

Bibliographie
Cité par

[C] J.R. Chen, On Goldbach's problem and the sieve methods. Sci. Sin., 21 (1978), 701-739. | Zbl | MR

[D] H. Davenport, Multiplicative Number Theory. 2nd ed., Springer, 1980. | Zbl | MR

[G] P.X. Gallagher, Primes and powers of 2. Invent. Math. 29(1975), 125-142. | Zbl | MR

[HL] G.H. Hardy and J.E. Littlewood, 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

[HR] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, 1974. | Zbl | MR

[KPP] J. Kaczorowski, A. Perelli and J. Pintz, A note on the exceptional set for Goldbach's problem in short intervals. Mh. Math. 116 (1993), 275-282; corrigendum 119 (1995), 215-216.

[L1] Yu. V. Linnik, Prime numbers and powers of two. Trudy Mat. Inst. Steklov 38 (1951), 151-169. | Zbl | MR

[L2] Yu.V. Linnik, Addition of prime numbers and powers of one and the same number. Mat. Sb.(N. S.) 32 (1953), 3-60. | Zbl | MR

[LLW1] J.Y. Liu, M.C. Liu, and T.Z. Wang, The number of powers of 2 in a representation of large even integers (I). Sci. China Ser. A 41 (1998), 386-398. | Zbl | MR

[LLW2] J.Y. Liu, M.C. Liu, and T.Z. Wang, The number of powers of 2 in a representation of large even integers (II). Sci. China Ser. A. 41 (1998), 1255-1271. | Zbl | MR

[LP] A. Languasco and A. Perelli, A pair correlation hypothesis and the exceptional set in Goldbach's problem. Mathematika 43 (1996), 349-361. | Zbl | MR

[P] K. Prachar, Primzahlverteilung. Springer, 1957. | Zbl | MR

[R] N.P. Romanoff, Über einige Sätze der additiven Zahlentheorie. Math. Ann. 109 (1934), 668-678. | Zbl | MR | JFM

[RS] J.B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), 64-94. | Zbl | MR

[Vi] A.I. Vinogradov, On an "almost binary" problem. Izv. Akad. Nauk. SSSR Ser. Mat. 20 (1956), 713-750. | Zbl | MR