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

Cantarini, Marco; Gambini, Alessandro; Zaccagnini, Alessandro

doi:10.1090/proc/14827

On the average number of representationsof an integer as a sum of like prime powers
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by Marco Cantarini, Alessandro Gambini and Alessandro Zaccagnini PDF

Proc. Amer. Math. Soc. 148 (2020), 1499-1508 Request permission

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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