On the oscillatory behavior of certain arithmetic functions associated with automorphic forms (Q640021)

In this work, the author derives some results related to oscillatory behavior of certain arithmetic functions associated with automorphic forms. Specifically, he examines general \(L\)-functions conjectured to satisfy the Grand Riemann Hypothesis, Dirichlet series associated with classical entire forms of real weight and multiplier system, Rankin-Selberg convolutions (both ``naive'' and ``modified''), and spinor zeta-functions of Hecke eigenforms on the Siegel modular group of genus two. For the second class he extends results obtained previously and jointly by M. Knopp, W. Kohnen, and the author, whereas for the fourth class he provides a new proof of a relatively recent result of W. Kohnen.