Zeros on the critical line of Dirichlet series associated with Hilbert modular forms

The relation is studied between the behavior of Hilbert modular forms in a neighborhood of some manifold and the zeros on the critical line of the associated Dirichlet series. The results are applied to Eisenstein series associated with quadratic forms over real quadratic fields.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 76, pp. 89–123, 1978.