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The Addition of Primes and Power

  • Jörg Brüdern (a1) and Alberto Perelli (a2)

Abstract

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.

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References

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1. Brüdern, J., A problem in additive number theory, Math. Proc. Cambridge Philos. Soc. 103 (1988), 2733.
2. Brünner, R., Perelli, A. and Pintz, J., The exceptional set for the sum of a prime and a square, Acta Math. Hungar. 53 (1989), 347365.
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The Addition of Primes and Power

  • Jörg Brüdern (a1) and Alberto Perelli (a2)

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