Divisor problem in special sets of Gaussian integers

Abstract

DIVISOR PROBLEM IN SPECIAL SETS OF GAUSSIAN INTEGERSLet A 1 and A 2 be fixed sets of gaussian integers. We denote by τ A 1 ,A 2 (ω) the number of representations of ω in form ω = αβ, where α ∈ A 1 , β ∈ A 2 . We construct the asymptotical formula for summatory function τ A 1 ,A 2 (ω) in case, when ω lie in the arithmetic progression, A 1 is a fixed sector of complex plane, A 2 = Z[i].