Research on additive problems concerning powers of primes.

我们发现在某些情况下，Davenport的范围递减方法对Wooley方法的应用有显著的影响，Wooley方法提供了与加性问题相关的异常集的尖锐估计。这种方法可以应用于各种类型的可加性问题，其中，我们建立了与素数的立方或双方和相关的异常集的新估计。同时，我们证明了每一个足够大的整数都可以写成八个最多有两个质因数的自然数的立方数的和。

We discovered that under certain circumstances, Davenport's diminishing range method has significant effects on the application of Wooley's method which provides sharp estimates for exceptional sets associated with additive problems. This method may be applied to various kinds of additive problems, and amongst others, we established new estimates for exceptional sets associated with sums of cubes, or biquadrates, of prime numbers. Also, we showed that every sufficiently large integer can be written as the sums of eight cubes of natural numbers that has at most two prime factors.