素变量混合幂丢番图不等式

Mixed Variables Diophantine Inequality with Prime Variables

设η是任意给定的实数,λ_1,λ_2,λ_3,λ_4是非零实数不全同号,并且λ_1/λ_2是无理数,素变量P_j满足不等式|λ1p1+λ2p22+λ3p32+λ4p43+η|≤(max pj)-σ在有无穷多组素数解的情况下σ的值.使用Davenport-Heilbronn方法来计算,得到结果 maxPj的指数估计为σ=9/48+ε,ε>0.

Let η be any real number,suppose that λ_1,λ_2,λ_3,λ_4 are nonzero real numbers,not all of the same sign and λ_1/λ_2 is irrational. Prime variables Pjto meet that the inequality |λ1p1+ λ2p22+ λ3p32+ λ4p43+ η| ≤( max pj)-σhas infinitely many solutions,in case of σ's solution. Using Davenport-Heilbronn method and the index max Pjis σ =9/48+ ε for any ε > 0.