The correspondence between theta series of ternary and quaternary quadratic forms

This article uses orthogonal groups and quaternion algebras to describe the Shimura lifting for theta series of general three-dimensional lattices with spherical coefficients.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniye Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 196, pp. 61–82, 1991.