Research on additive problems concerning powers of primes.

我们发现，在某些情况下，达文波特的递减范围方法对伍利方法的应用有显着影响，伍利方法为与加性问题相关的异常集提供了敏锐的估计。该方法可以应用于各种加性问题，除此之外，我们还为与素数的立方和或二二阶之和相关的特殊集合建立了新的估计。此外，我们还表明，每个足够大的整数都可以写成最多有两个质因数的八个自然数立方的和。

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.