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

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

2003-07-16

arxiv.org/abs/math/0307221v1

Acta Math. Hung. 104 (2004), 225-240

Mathematics

Number Theory

Scientific paper

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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