1. Department of Mathematics and Information Science, He'nan University of Economics and Law, Zhengzhou 450002, P. R. China;
2. School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, P. R. China
{{custom_zuoZheDiZhi}}
{{custom_authorNodes}}
{{custom_bio.content}}
{{custom_bio.content}}
{{custom_authorNodes}}
Collapse
文章历史+
收稿日期
修回日期
出版日期
2014-06-27
2014-12-31
2015-09-15
发布日期
2015-09-15
摘要
证明了整系数素变数方程a1p1+a2p22+a3p32+a4p42 = b 当整数 a1,..., a4, b满足一定条件时有素数解, 并给出了此方程有素数解时小素数解的上界.
Abstract
The present paper proved that the prime variables of nonlinear equation a1p1+a2p22+a3p32+a4p42 = b is soluble if integers a1,...,a4, b satisfy certain conditions, and it gave the upper bound for small prime solutions.
Wei Ping LI, Feng ZHAO, Tian Ze WANG.
Small Prime Solutions of an Nonlinear Equation. Acta Mathematica Sinica, Chinese Series, 2015, 58(5): 739-764 https://doi.org/10.12386/A2015sxxb0075
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Baker A., On some diophantine inequalities involving primes, J. Reine Angew. Math., 1967, 228: 166-181.
[2] Choi K. K. S., A numerical Baker's constant-Some explicit estimates for small prime solutions of linear equations, Bull. Hong Kong Math. Soc., 1997, 1: 1-19.
[3] Choi K. K. S., Liu M. C., Tsang K. M., Conditional bounds for small prime solutions of linear equations, Manuscripta Math., 1992, 74: 321-340.
[4] Davenport H., Multiplicative Number Theory, 2nd ed., Graduate Text in Math., Vol. 74, Spring-Verlag, New York, 1980.
[5] Graham S., Applications of Sieve Methods, Ph.D. Thesis, University of Michigan, Ann Arbor, 1977.
[6] Hua L. K., Some results in the additive prime number theory, Quart. J. Math. Oxford, 1938, 9: 68-80.
[7] Liu M. C., A bound for prime solutions of some ternary equations, Math. Z., 1985, 188: 313-323.
[8] Liu M. C., An improved bound for prime solutions of some ternary equations, Math. Z., 1987, 194: 573-583.
[9] Liu M. C., Tsang K. M., Small prime solutions of linear equations, Théorie des Nombres, J. M. De Koninck and C. Levesque (eds.), de Gruyter, Berlin, 1989: 595-624.
[10] Liu M. C., Tsang K. M., Recent progress on a problem of A. Baker, Séminaire de Théorie des Nombres, Paris, 1991-1992, Progr. Math. 116, Birkhäuser, 1993: 121-133.
[11] Liu M. C., Tsang K. M., Small prime solutions of some additive equations, Mh. Math., 1991, 111: 147-169.
[12] Liu M. C., Tsang K. M., On pairs of linear equations in three primes variables and an application to Goldbach's problem, J. Reine Angew. Math., 1989, 399: 109-136.
[13] Liu M. C., Wang T. Z., A numerical bound for small prime solutions of some ternary linear equations, Acta Arithmetica, 1998, 86(4): 343-383.
[14] Liu M. C., Wang T. Z., Wang Y., A numerical bound for small prime solutions of some ternary linear equations, II Asian J. Math., 2000, 4(4): 961-976.
[15] Vinogradov I. M., Representation of an odd number as the sums of three primes, Dokl. Akad. Nauk, 1937, SSSR, 15: 291-294.
[16] Wang T. Z., Chen J. R., On estimation of linear trigonometrical sums with primes, Acta Mathematica Sinica, Chinese Series, 1994, 37(1): 25-31.
[17] Xu Y. F., On sums of one prime and three squares of primes in short intervals, Acta Mathematica Sinica, Chinese Series, 2009, 52(3): 457-470.