In the present paper, we use Ramachandra's kernel function of the second order, namely Exp((sinz)2), which has some advantages over the earlier kernel Exp(z4a+2) where a is a positive integer. As an outcome of the new kernel we are able to handle Ω-theorems for error terms in the asymptotic formula for the summatory function of the coefficients of generating functions of the Exp(ζ(s)),ExpExp(ζ(s)) and also of the type ExpExp((ζ(s))12).
Let f be a binary form of degree l≥3, that is, a product of linear forms with integer coefficients. The principal result of this paper is an asymptotic formula of the shape n2/l(C(f)+O(n−ηl+ε)) for the number of positive integers not exceeding n that are representable by f; here C(f)>0 and ηl>0.