Nonhomogeneous Rankin convolutions

The properties of the Rankin convolutions of two eigenfunctions of different parities from the discrete part of the spectrum of the Laplace operator are studied. Analytical continuability of these convolutions into the left half-plane is proved and a functional equation of Riemann type is obtained. Applications to arithmetical convolutions are given. In particular the asymptotics of such convolutions is obtained by using the nonhomogeneous Rankin convolutions. Bibl. 4 titles.