New omega results in a weighted divisor problem

Abstract

New omega results are given for the error term in a weighted divisor problem, improving results of Schierwagen. The Ω+ result is improved (surprisingly, perhaps) by a logarithm factor in all cases. The methods are similar to earlier results of the author for Dirichlet's divisor problem and in fact, with a slight modification of the argument, include that result as a special case. The Ω- result is improved by an exponential of iterated logarithms, similar to results of Kátai and Corrádi, and Joris and Redmond. Both results rely on a Voronoi-type identity for the error term due to Krätzel. © 1988.