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The Addition of Primes and Power

Published online by Cambridge University Press:  20 November 2018

Jörg Brüdern  and
Alberto Perelli
Jörg Brüdern
Affiliation:
Mathematisches Institut A Pfaffenwaldring 57 D-70511 Stuttgart Germany
Alberto Perelli
Affiliation:
Dipartimento di Matematica Via Dodecaneso 35 1-16146 Genova e-mail: [email protected] e-mail: [email protected]
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Abstract

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Let k ≥ 2 be an integer. Let Ek(N) be the number of natural numbers not exceeding N which are not the sum of a prime and a k-th power of a natural number. Assuming the Riemann Hypothesis for all Dirichlet L-functions it is shown that Ek(N) ≪ N1-1/25k.

Keywords

11P55
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 3 , 01 June 1996 , pp. 512 - 526
Copyright
Copyright © Canadian Mathematical Society 1996

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