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On the average number of representations of an integer as a sum of like prime powers (1805.09008v3)
Published 23 May 2018 in math.NT
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 last Author, which dealt with the case $k = 2$ [6] and $k = 3$ [5] respectively. We use the same technique to study the corresponding problem for sums of just $k$ perfect $k$-th powers of primes.