  We derive a Voronoi-type series approximation for the local weighted mean of
an arithmetical function that is associated to Dirichlet series satisfying a
functional equation with gamma factors. The series is exploited to study the
oscillation frequency with a method of Heath-Brown and Tsang [7]. A by-product
is another proof for the well-known result of no element in the Selberg class
of degree 0 \textless{} d \textless{} 1. Our major applications include the
sign-change problem of the coefficients of automorphic L-functions for GL m ,
which improves significantly some results of Liu and Wu [14]. The cases of
modular forms of half-integral weight and Siegel eigenforms are also
considered.
