Arithmetic-analytic properties of binary positive-definite quadratic forms

One considers the arithmetic and analytic properties of positive-definite binary quadratic forms of discriminant –Dn². The arithmetic structure of the set of these forms is described by forms of discriminant –D and by the Hecke operators T(n). One gives some arithmetic and analytic consequences.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 5–20, 1985.