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On the exceptional set for the sum of a prime and a k-th power

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  26 February 2010

Alessandro Zaccagnini
Alessandro Zaccagnini
Affiliation:
Dipartimento di Matematica, Università di Genova, Via L. B. Alberti 4, 16132 Genova, Italy.
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Abstract

Let k ≤ 2 be an integer, and set

Ek (X) = |{n ≤ X, n ≠ mk, n not a sum of a prime and a k-th power}|.

We prove that there exists δ = δ(k) > 0 such that Ek (X)Ek(X)≪kX1−δ.

MSC classification

Secondary: 11P32: Goldbach-type theorems; other additive questions involving primes
Type
Research Article
Information
Mathematika , Volume 39 , Issue 2 , December 1992 , pp. 400 - 421
Copyright
Copyright © University College London 1992

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