Volume 25 - 2002


1. Some problems of Analytic number theory IV

R Balasubramanian ; K Ramachandra.
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).

2. On totally reducible binary forms: II.

C Hooley.
Let f be a binary form of degree l3, 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(nηl+ε)) for the number of positive integers not exceeding n that are representable by f; here C(f)>0 and ηl>0.