Reprsentations of Natural Numbers as the Sum of a Prime and a k-th Power

摘要

Subject to the Riemann hypothesis for Dirichlet L-functions an asymptotic formula is obtained for the number of representations of a natural number n as the sum of a prime and a k-th power, valid for almost n. Estimates for the error term in the asymptotic formula as well as for the size of the exceptional set are of a smaller order of magnitude than was known previously.