Korean Journal of Mathematics

  • 제24권1호
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  • Pages.107-138
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  • 2016
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ALMOST-PRIMES REPRESENTED BY p + am

  • Lu, Yaming (School of Mathematics and Statistics Xi'an Jiaotong University)
  • 투고 : 2015.03.19
  • 심사 : 2016.03.14
  • 발행 : 2016.03.30
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⟨ 이전 논문 다음 논문 ⟩

초록

Let $a{\geqslant}2$ be a xed integer in this paper. By using the method of Goldston, Pintz and Yildirm, we will prove that there are innitely many almost-primes which can be represented as $p+a^m$ in at least two dierent ways.

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과제정보

연구 과제 주관 기관 : N.S.F.

참고문헌

  1. Y. G. Chen and X. G. Sun, On Romanoff's constant, J. Number Theory 106 (2004), 275-284. https://doi.org/10.1016/j.jnt.2003.11.009
  2. P. Erdos, On integers of the form $2^k$ + p and some related problems, Summa Brasil. Math. 2 (1950), 113-123.
  3. J. B. Friedlander and H. Iwaniec, Hyperbolic prime number theorem, Acta Math. 202 (2009), 1-19. https://doi.org/10.1007/s11511-009-0033-z
  4. J. B. Friedlander and H. Iwaniec, Opera de Cribro, Colloquium Publications (vol.57), American Mathematical Society, Providence, Rhode Island, 2010.
  5. D. A. Goldston, J. Pintz, and C. Y. Yildirim, Primes in tuples I, Ann. of Math. 170 (2009), 819-862. https://doi.org/10.4007/annals.2009.170.819
  6. L. Habsieger, X. Roblot, On integers of the form p+$2^k$, Acta Arith. 122 (2006), 45-50. https://doi.org/10.4064/aa122-1-4
  7. J. Pintz, A note on Romanoff's constant, Acta Math. Hungar. 112 (2006), 1-14. https://doi.org/10.1007/s10474-006-0060-6
  8. K. Prachar, Uber einen Satz der additiven Zahlentheorie, Monatsh. Math. 56 (1952), 101-104. https://doi.org/10.1007/BF01412828
  9. N. P. Romanoff, Uber einige Satze der additiven Zahlentheorie, Math. Ann. 109 (1934), 668-678. https://doi.org/10.1007/BF01449161
  10. K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc. 44 (2007), 1-18.