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arXiv · 1806.05175

A Ces\`aro Average of generalised Hardy-Littlewood numbers

Alessandro Languasco·Alessandro Zaccagnini
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Abstract

We continue our recent work on additive problems with prime summands: we already studied the \emph{average} number of representations of an integer as a sum of two primes, and also considered individual integers. Furthermore, we dealt with representations of integers as sums of powers of prime numbers. In this paper, we study a Ces\`aro weighted partial \emph{explicit} formula for generalised Hardy-Littlewood numbers (integers that can be written as a sum of a prime power and a square) thus extending and improving our earlier results.

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Alessandro Languasco, Alessandro Zaccagnini. 2018-06-13. A Ces\`aro Average of generalised Hardy-Littlewood numbers. https://doi.org/10.2996/kmj/1562032834

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