The average number of solutions of the Diophantine equation U2 + V2 = W3 and related arithmetic functions
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 r2(n) and r(n3), where r(m) denotes the number of ways to write m as a sum of two squares of integers.
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