On sums and differences of two relative prime cubes, II

Rok, strany: 1997, 23 - 34

This article is concerned with the average order of the arithmetic functions $ρ₃⁺(n)$ and $ρ₃^-(n)$, which count the number of ways to write a natural number $n$ as the sum and the difference of two cubes of relative prime positive integers, respectively. Refining the argument of part I of this work, it is proved that

$$ ∑_{n≤ x} ρ₃pm (n) = A x^2=/3 + Bpm x^1=/2 + O(x^{((538) / (1857))+epsilon})    (epsilon>0) $$

(with explicit constants $A$, $B⁺$, and $B^-$), under the assumption that the Riemann Hypothesis is true.

ISO 690:

Nowak, W. 1997. On sums and differences of two relative prime cubes, II. In Tatra Mountains Mathematical Publications, vol. 11, no.2, pp. 23-34. 1210-3195.

APA:

Nowak, W. (1997). On sums and differences of two relative prime cubes, II. Tatra Mountains Mathematical Publications, 11(2), 23-34. 1210-3195.