PDF(395 KB)
PDF(395 KB)
PDF(395 KB)
幂次为2,3,4,5的素变量非线性型的整数部分
The Integer Part of Nonlinear Form with Mixed Powers 2, 3, 4, 5 and Prime Variables
考虑了一个混合幂次为2，3，4，5的素变量非线性型的整数部分表示无穷多素数的问题.运用Davenport-Heilbronn方法证明了：如果λ1，λ2，λ3，λ4是正实数，至少有一个λi/λj（1≤i< j≤4）是无理数，那么存在无穷多素数p1，p2，p3，p4，p，使得[λ1p12+λ2p23+λ3p34+λ4p45]=p.
The present paper considered one problem which integer part of nonlinear form with mixed powers 2, 3, 4, 5 and prime variables represents prime infinitely. Using Davenport-Heilbronn method, we show that if λ1,λ2,λ3,λ4 are positive real numbers,at least one of the ratios λi/λj (1≤i< j≤4) is irrational, then there exist infinitely many primes p1,p2,p3,p4,p such that[λ1p12+λ2p23+λ3p34+λ4p45]=p.
素数变量 / 丢番图逼近 / Davenport-Heilbronn方法 {{custom_keyword}} /
prime variables / diophantine approximation / Davenport-Heilbronn method {{custom_keyword}} /
[1] Danicic I., On the integral part of a linear form with prime variables, Canadian J. Math., 1966, 18:621-628.
[2] Davenport H., Roth K. F., The solubility of certain diophantine inequalities, Mathematika, 1955, 2:81-96.
[3] Harman G., Trigonometric sums over primes I, Mathematika, 1981, 28:249-254.
[4] Li W. P., Su B. Y., The integral part of a nonlinear form with five cubes of primes, Lithuanian Mathematical J., 2013, 53:63-71.
[5] Li W. P., Wang T. Z., The integral part of a nonlinear form with three squares of primes (in Chinese), Chinese Annals of Math., 2011, 32(6):753-762.
[6] Li W. P., Wang T. Z., The integral part of nonlinear form with k powers of primes, Acta Mathematica Sinica, Chinese Series, 2013, 56(4):605-612.
[7] Vaughan R. C., Diophantine approximation by prime numbers, I, Proc. London Math. Soc., 1974, 28:373-384.
[8] Vaughan R. C., Diophantine approximation by prime numbers, Ⅱ, Proc. London Math. Soc., 1974, 28:385-401.
[9] Vaughan R. C., The Hardy-Littlewood Method, Second Edition, Cambridge Tracts in Mathematics, Vol. 125, Cambridge University Press, Cambridge, 1997.
国家自然科学基金资助项目（11371122，11471112）；2011河南省创新型科技人才队伍建设工程；2013年河南省科技创新杰出人才，河南省科技攻关项目（152102310320）
/
| 〈 |
|
〉 |
