Abstract
We consider a class of arithmetical functions generated by Dirichlet series that satisfy a functional equation with multiple gamma factors. We prove one- and two-sided omega theorems for the error terms associated with summatory functions of the type Σ λ n ≤ x a( n)( x − λ n ) ϱ , where ϱ ≥ 0. In particular, we improve results of Hardy for the circle and Dirichlet divisor problems and results of Szegö and Walfisz for the Piltz divisor problem in algebraic number fields.
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