On the almost Goldbach problem of Linnik

Jianya Liu; Ming-Chit Liu; Tianze Wang

Journal de théorie des nombres de Bordeaux (1999)

  • Volume: 11, Issue: 1, page 133-147
  • ISSN: 1246-7405

Abstract

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

How to cite

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Liu, Jianya, Liu, Ming-Chit, and Wang, Tianze. "On the almost Goldbach problem of Linnik." Journal de théorie des nombres de Bordeaux 11.1 (1999): 133-147. <http://eudml.org/doc/248325>.

@article{Liu1999,
abstract = {Under the Generalized Riemann Hypothesis, it is proved that for any $k \ge 200$ there is $ N_k &gt; 0$ depending on $k$ only such that every even integer $\ge N_k$ is a sum of two odd primes and $k$ powers of $2$.},
author = {Liu, Jianya, Liu, Ming-Chit, Wang, Tianze},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {almost Goldbach problem; generalized Riemann hypothesis},
language = {eng},
number = {1},
pages = {133-147},
publisher = {Université Bordeaux I},
title = {On the almost Goldbach problem of Linnik},
url = {http://eudml.org/doc/248325},
volume = {11},
year = {1999},
}

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
PB - Université Bordeaux I
VL - 11
IS - 1
SP - 133
EP - 147
AB - Under the Generalized Riemann Hypothesis, it is proved that for any $k \ge 200$ there is $ N_k &gt; 0$ depending on $k$ only such that every even integer $\ge N_k$ is a sum of two odd primes and $k$ powers of $2$.
LA - eng
KW - almost Goldbach problem; generalized Riemann hypothesis
UR - http://eudml.org/doc/248325
ER -

References

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  2. [D] H. Davenport, Multiplicative Number Theory. 2nd ed., Springer, 1980. Zbl0453.10002MR606931
  3. [G] P.X. Gallagher, Primes and powers of 2. Invent. Math.29(1975), 125-142. Zbl0305.10044MR379410
  4. [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. JFM49.0127.03
  5. [HR] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, 1974. Zbl0298.10026MR424730
  6. [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. Zbl0792.11040
  7. [L1] Yu. V. Linnik, Prime numbers and powers of two. Trudy Mat. Inst. Steklov38 (1951), 151-169. Zbl0049.31402MR50618
  8. [L2] Yu.V. Linnik, Addition of prime numbers and powers of one and the same number. Mat. Sb.(N. S.) 32 (1953), 3-60. Zbl0051.03402MR59938
  9. [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.A41 (1998), 386-398. Zbl1029.11049MR1663182
  10. [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. Zbl0924.11086MR1681935
  11. [LP] A. Languasco and A. Perelli, A pair correlation hypothesis and the exceptional set in Goldbach's problem. Mathematika43 (1996), 349-361. Zbl0884.11042MR1433280
  12. [P] K. Prachar, Primzahlverteilung. Springer, 1957. Zbl0080.25901MR87685
  13. [R] N.P. Romanoff, Über einige Sätze der additiven Zahlentheorie. Math. Ann.109 (1934), 668-678. Zbl0009.00801MR1512916JFM60.0131.03
  14. [RS] J.B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers. Illinois J. Math.6 (1962), 64-94. Zbl0122.05001MR137689
  15. [Vi] A.I. Vinogradov, On an "almost binary" problem. Izv. Akad. Nauk. SSSR Ser. Mat.20 (1956), 713-750. Zbl0072.27001MR87686

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