A two-sided omega-theorem for an asymmetric divisor problem

In this article we study the arithmetic functiond _a,b (l,k;n) which is defined as the number of representationsn=v ^a w ^b withw lying in the residue classl modulok (a,b andl,k fixed positive integers). For the remainder term in the asymptotic formula for Σ_n≤xd_a,b(l,k,;n) we obtain an Ω_± (under a certain restriction onl andk) which is sharper than the known results for the corresponding “unrestricted” problem.