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The average number of solutions of the Diophantine equation U^2 + V^2 = W^3 and related arithmetic functions

Manfred K"\uhleitner·Werner Georg Nowak
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Abstract

This paper provides asymptotics with a sharp error term for the Dirichlet summatory function of a certain class of arithmetic functions. The result applies, e.g., to the sums over r^2(n) and r(n^3), where r(m) denotes the number of ways to write m as a sum of two squares of integers.

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Manfred K"\uhleitner, Werner Georg Nowak. 2003-07-16. The average number of solutions of the Diophantine equation U^2 + V^2 = W^3 and related arithmetic functions. https://arxiv.org/abs/math/0307221

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