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

Acta Arithmetica (1998)

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

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topMing-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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- [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
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- [G2] S. Graham, On Linnik's constant, Acta Arith. 39 (1981), 163-179.
- [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
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- [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.
- [Li1] M. C. Liu, A bound for prime solutions of some ternary equations, Math. Z. 188 (1985), 313-323.
- [Li2] M. C. Liu, An improved bound for prime solutions of some ternary equations, ibid. 194 (1987), 573-583.
- [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.
- [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
- [PP] C. D. Pan and C. B. Pan, Goldbach Conjecture (English version), Science Press, Beijing, 1992.

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