A numerical bound for small prime solutions of some ternary linear equations
Ming-Chit Liu ; Tianze Wang
Acta Arithmetica, Tome 84 (1998), p. 343-383 / Harvested from The Polish Digital Mathematics Library
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207201
@article{bwmeta1.element.bwnjournal-article-aav86i4p343bwm,
     author = {Ming-Chit Liu and Tianze Wang},
     title = {A numerical bound for small prime solutions of some ternary linear equations},
     journal = {Acta Arithmetica},
     volume = {84},
     year = {1998},
     pages = {343-383},
     zbl = {0918.11053},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav86i4p343bwm}
}
Ming-Chit Liu; Tianze Wang. A numerical bound for small prime solutions of some ternary linear equations. Acta Arithmetica, Tome 84 (1998) pp. 343-383. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav86i4p343bwm/

[000] [B] A. Baker, On some diophantine inequalities involving primes, J. Reine Angew. Math. 228 (1967), 166-181. | Zbl 0155.09202

[001] [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. | Zbl 0417.10038

[002] [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. | Zbl 0938.11047

[003] [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. | Zbl 0753.11033

[004] [D] H. Davenport, Multiplicative Number Theory, 2nd ed., Grad. Texts in Math. 74, Springer, 1980. | Zbl 0453.10002

[005] [G1] S. Graham, Applications of sieve methods, Ph.D. thesis, University of Michigan, 1977.

[006] [G2] S. Graham, On Linnik's constant, Acta Arith. 39 (1981), 163-179.

[007] [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. | Zbl 0739.11033

[008] [J] M. Jutila, On Linnik's constant, Math. Scand. 41 (1977), 45-62. | Zbl 0363.10026

[009] [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. | Zbl 0063.03584

[010] [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.

[011] [Li1] M. C. Liu, A bound for prime solutions of some ternary equations, Math. Z. 188 (1985), 313-323.

[012] [Li2] M. C. Liu, An improved bound for prime solutions of some ternary equations, ibid. 194 (1987), 573-583.

[013] [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.

[014] [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. | Zbl 0826.11045

[015] [PP] C. D. Pan and C. B. Pan, Goldbach Conjecture (English version), Science Press, Beijing, 1992.