## Tsukuba Journal of Mathematics

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

Jörg Brüdern

#### 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.

#### Article information

Source
Tsukuba J. Math., Volume 32, Number 2 (2008), 349-360.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496165235

Digital Object Identifier
doi:10.21099/tkbjm/1496165235

Mathematical Reviews number (MathSciNet)
MR2477986

Zentralblatt MATH identifier
1307.11103

#### Citation

Brüdern, Jörg. Reprsentations of Natural Numbers as the Sum of a Prime and a $k$-th Power. Tsukuba J. Math. 32 (2008), no. 2, 349--360. doi:10.21099/tkbjm/1496165235. https://projecteuclid.org/euclid.tkbjm/1496165235