On an asymmetric divisor problem with congruence conditions

For fixed positive integersab, natural numbersl₁k₁,l₂k₂ andn, denote withd_a,b(l₁,k₁;l₂,k₂;n) the number of all (,)N² with^ab=n,l₁(modk₁),l₂(modk₂). In the present paper we establish asymptotic formulas for the Dirichlet summatory function ofd_a,b(l₁,k₁;l₂,k₂;n) with both upper and lower estimates of the error term, all of them uniform in the moduli.