On the average number of representationsof an integer as a sum of like prime powers

2019/09/04 by Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini · 1 citation
Mathematics · Computer Science · #Analytic Number Theory Research #Graph Labeling and Dimension Problems #Advanced Mathematical Identities

paper · doi:10.1090/proc/14827

Abstract

We investigate the average number of representations of a positive integer as the sum of k + 1 perfect k-th powers of primes. We extend recent results of Languasco and the third author, which dealt with the case k = 2 and k = 3, respectively. We use the same technique to study the corresponding problem for sums of just k perfect k-th powers of primes.

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