Short mean values of products of multiplicative functions
by
Stephan Daniel
Cardiff University, Wales

We state a general upper bound for mean values of the type \sum_{x-y < n <= x} f₁(k₁ n + l₁) ... f_r(k_r n + l_r), where f_i are multiplicative arithmetic functions with reasonable properties and where max(k_i, l_i) << logx << logy. This generalizes a well-known result of Shiu for r=1. We further indicate a generalization, where the arguments are replaced by values of polynomials of higher degree. This makes a recent result of Nair and Tenenbaum more explicit in terms of the resultants of the involved polynomials.

Date received: February 23, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadx-32.