Kodai Mathematical Journal

A Cesàro average of generalised Hardy-Littlewood numbers

Alessandro Languasco and Alessandro Zaccagnini

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We continue our recent work on additive problems with prime summands: we already studied the 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 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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Kodai Math. J., Volume 42, Number 2 (2019), 358-375.

First available in Project Euclid: 2 July 2019

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Languasco, Alessandro; Zaccagnini, Alessandro. A Cesàro average of generalised Hardy-Littlewood numbers. Kodai Math. J. 42 (2019), no. 2, 358--375. doi:10.2996/kmj/1562032834. https://projecteuclid.org/euclid.kmj/1562032834

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