A Cesàro Average of generalised Hardy-Littlewood numbers
arXiv:1806.05175 · doi:10.2996/kmj/1562032834
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 Cesàro 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.
to appear in Kodai Mathematical Journal. arXiv admin note: substantial text overlap with arXiv:1206.0255