幂次为3和4的整数变量非线性型的整数部分

The integer parts of a nonlinear form with integer variables and powers 3 and 4

本文利用Davenport-Heilbronn方法证明了对于自然数xj,表达式λ1x31+λ2x32+λ3x33+λ4x44+λ5x45+λ6x46的整数部分在给定条件下可表示无穷多素数,深化了Brüdern等人的广义Riemann假设下等幂次的结果.

In this note, using the Davenport-Heilbronn circle method, we proved that under certain conditions the integer parts of λ1x1^3＋λ2x2^3＋λ3x3^3＋λ4x4^4＋λ5x5^4＋λ6x6^4 are prime infinitely often for natural numbers x j . This result deepens Brüdern’s conclusion which is under general Riemann Hypothesis and same powers.