Abstract
Let ψG(xt, x) denote the number of Gaussian integers with norm not exceeding x2t whose Gaussian prime factors have norm not exceeding x2. Previous estimates have required restrictions on the parameter t with respect to x. The purpose of this note is to present asymptotic estimates for ψG(xt, x) for all ranges of the parameter t with respect to x.
Highlights
Previous estimates have required restrictions on the parameter t with respect to x
Throughout the discussion the0-notatlon the constants implied by the use of will be absolute unless otherwise indicated
The purpose of this note is to present an asymptotic estimate for all ranges of the parameter t with respect to x
Summary
Previous estimates have required restrictions on the parameter t with respect to x. Let denote the number of Gausslan integers with norm not exceeding Let denote a Gaussian integer, p a Gaussian prime, N H. Jordan [3] and the author [2] gave asymptotic estimates for the number of Gausslan integers with norms not exceeding x2t having only
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