Abstract
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.
Citation
Jörg Brüdern. "Reprsentations of Natural Numbers as the Sum of a Prime and a $k$-th Power." Tsukuba J. Math. 32 (2) 349 - 360, December 2008. https://doi.org/10.21099/tkbjm/1496165235
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