Under the Generalized Riemann Hypothesis, it is proved that for any there is depending on only such that every even integer is a sum of two odd primes and powers of .
On démontre que sous GRH et pour , tout entier pair assez grand est somme de deux nombres premiers impairs et de puissances de .
@article{JTNB_1999__11_1_133_0, author = {Liu, Jianya and Liu, Ming-Chit and Wang, Tianze}, title = {On the almost {Goldbach} problem of {Linnik}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {133--147}, publisher = {Universit\'e Bordeaux I}, volume = {11}, number = {1}, year = {1999}, mrnumber = {1730436}, zbl = {0979.11051}, language = {en}, url = {http://www.numdam.org/item/JTNB_1999__11_1_133_0/} }
TY - JOUR AU - Liu, Jianya AU - Liu, Ming-Chit AU - Wang, Tianze 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 - http://www.numdam.org/item/JTNB_1999__11_1_133_0/ LA - en ID - JTNB_1999__11_1_133_0 ER -
Liu, Jianya; Liu, Ming-Chit; Wang, Tianze. On the almost Goldbach problem of Linnik. Journal de théorie des nombres de Bordeaux, Volume 11 (1999) no. 1, pp. 133-147. http://www.numdam.org/item/JTNB_1999__11_1_133_0/
[C] On Goldbach's problem and the sieve methods. Sci. Sin., 21 (1978), 701-739. | MR | Zbl
,[D] Multiplicative Number Theory. 2nd ed., Springer, 1980. | MR | Zbl
,[G] Primes and powers of 2. Invent. Math. 29(1975), 125-142. | MR | Zbl
,[HL] 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
and ,[HR] Sieve Methods, Academic Press, 1974. | MR | Zbl
and ,[KPP] A note on the exceptional set for Goldbach's problem in short intervals. Mh. Math. 116 (1993), 275-282; corrigendum 119 (1995), 215-216.
, and ,[L1] Prime numbers and powers of two. Trudy Mat. Inst. Steklov 38 (1951), 151-169. | MR | Zbl
,[L2] Addition of prime numbers and powers of one and the same number. Mat. Sb.(N. S.) 32 (1953), 3-60. | MR | Zbl
,[LLW1] The number of powers of 2 in a representation of large even integers (I). Sci. China Ser. A 41 (1998), 386-398. | MR | Zbl
, , and ,[LLW2] The number of powers of 2 in a representation of large even integers (II). Sci. China Ser. A. 41 (1998), 1255-1271. | MR | Zbl
, , and ,[LP] A pair correlation hypothesis and the exceptional set in Goldbach's problem. Mathematika 43 (1996), 349-361. | MR | Zbl
and ,[P] Primzahlverteilung. Springer, 1957. | MR | Zbl
,[R] Über einige Sätze der additiven Zahlentheorie. Math. Ann. 109 (1934), 668-678. | JFM | MR | Zbl
,[RS] Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), 64-94. | MR | Zbl
and ,[Vi] On an "almost binary" problem. Izv. Akad. Nauk. SSSR Ser. Mat. 20 (1956), 713-750. | MR | Zbl
,