A numerical bound for small prime solutions of some ternary linear equations

Ming-Chit Liu; Tianze Wang

Acta Arithmetica (1998)

  • Volume: 86, Issue: 4, page 343-383
  • ISSN: 0065-1036

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Ming-Chit Liu, and Tianze Wang. "A numerical bound for small prime solutions of some ternary linear equations." Acta Arithmetica 86.4 (1998): 343-383. <http://eudml.org/doc/207201>.

@article{Ming1998,
author = {Ming-Chit Liu, Tianze Wang},
journal = {Acta Arithmetica},
keywords = {ternary linear equations; Goldbach problem; small solutions; circle method; zeros of Dirichlet -functions; zero-free region},
language = {eng},
number = {4},
pages = {343-383},
title = {A numerical bound for small prime solutions of some ternary linear equations},
url = {http://eudml.org/doc/207201},
volume = {86},
year = {1998},
}

TY - JOUR
AU - Ming-Chit Liu
AU - Tianze Wang
TI - A numerical bound for small prime solutions of some ternary linear equations
JO - Acta Arithmetica
PY - 1998
VL - 86
IS - 4
SP - 343
EP - 383
LA - eng
KW - ternary linear equations; Goldbach problem; small solutions; circle method; zeros of Dirichlet -functions; zero-free region
UR - http://eudml.org/doc/207201
ER -

References

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  1. [B] A. Baker, On some diophantine inequalities involving primes, J. Reine Angew. Math. 228 (1967), 166-181. Zbl0155.09202
  2. [Che] J. R. Chen, On the least prime in an arithmetical progression and theorems concerning the zeros of Dirichlet's L-functions (II), Sci. Sinica 22 (1979), 859-889. Zbl0417.10038
  3. [Cho] K. K. S. Choi, A numerical bound for Baker's constant - some explicit estimates for small prime solutions of linear equations, Bull. Hong Kong Math. Soc. 1 (1997), 1-19. Zbl0938.11047
  4. [CLT] K. K. Choi, M. C. Liu and K. M. Tsang, Conditional bounds for small prime solutions of linear equations, Manuscripta Math. 74 (1992), 321-340. Zbl0753.11033
  5. [D] H. Davenport, Multiplicative Number Theory, 2nd ed., Grad. Texts in Math. 74, Springer, 1980. Zbl0453.10002
  6. [G1] S. Graham, Applications of sieve methods, Ph.D. thesis, University of Michigan, 1977. 
  7. [G2] S. Graham, On Linnik's constant, Acta Arith. 39 (1981), 163-179. 
  8. [H-B] D. R. Heath-Brown, Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression, Proc. London Math. Soc. 64 (1992), 265-338. Zbl0739.11033
  9. [J] M. Jutila, On Linnik's constant, Math. Scand. 41 (1977), 45-62. Zbl0363.10026
  10. [L] Yu. V. Linnik, On the least prime in an arithmetic progression (I, II), Rec. Math. (Mat. Sb.) N. S. 15 (57) (1944), 139-178; 347-368. Zbl0063.03584
  11. [LLW] 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, to appear. 
  12. [Li1] M. C. Liu, A bound for prime solutions of some ternary equations, Math. Z. 188 (1985), 313-323. 
  13. [Li2] M. C. Liu, An improved bound for prime solutions of some ternary equations, ibid. 194 (1987), 573-583. 
  14. [LT1] M. C. Liu and K. M. Tsang, Small prime solutions of linear equations, in: Théorie des Nombres, J.-M. De Koninck and C. Levesque (eds.), de Gruyter, Berlin, 1989, 595-624. 
  15. [LT2] M. C. Liu and K. M. Tsang, Recent progress on a problem of A. Baker, in: Séminaire de Théorie des Nombres, Paris 1991-1992, Progr. Math. 116, Birkhäuser, 1993, 121-133. Zbl0826.11045
  16. [PP] C. D. Pan and C. B. Pan, Goldbach Conjecture (English version), Science Press, Beijing, 1992. 

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