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On prime vs. prime power pairs

  • Yuta SuzukiEmail author
Article
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Abstract

In this paper, we consider pairs of a prime and a prime power with a fixed difference. We prove an average result on the distribution of such pairs. This is a partial improvement of the result of Bauer (Acta Arith. 85:99–118, 1998).

Keywords

Waring–Goldbach problem Circle method 

Mathematics Subject Classification

Primary 11P32 Secondary 11P55 

Notes

Acknowledgements

The author would like to thank Kohji Matsumoto, Hiroshi Mikawa, Koichi Kawada and Alberto Perelli for their helpful comments and suggestions. This work was supported by Grant-in-Aid for JSPS Research Fellow (Grant Number: JP16J00906).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityChikusa-ku, NagoyaJapan

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