论文标题
对角线解释系统的主要解决方案
Prime Solutions of Diagonal Diophantine Systems
论文作者
论文摘要
考虑一个一般的对角线系统的对角线系统。由于存在适当的平均值结合（和局部溶解度），因此找到了用于素溶液数量的渐近公式。这与vinogradov平均值定理结合使用，为Vinogradov Systems解决方案提供了渐近公式，并结合Hooley在七个立方体上的工作，以使Waring-Goldbach问题有条件地结果，这是对Hooley Hooley的七立方riemant o o riemann o reemann riemann for of to riemann riemann of riemann perfortent of the Waring-goldbach问题。
Consider a general diagonal system of Diophantine equations. Contingent on existence of an appropriate mean value bound (and local solvability), an asymptotic formula for the number of prime solutions is found. This is used in conjunction with the Vinogradov Mean Value Theorem to give an asymptotic formula for solutions of Vinogradov systems, and in conjunction with Hooley's work on seven cubes to give a conditional result for the Waring-Goldbach problem on seven cubes of primes, contingent on Hooley's form of Riemann hypothesis.
