Modular forms of varying weight. II
This note is a continuation of part I [ibid. 190, 477-495 (1985; Zbl 0553.10021)]. For the full modular group meromorphic families of modular forms in two variables (r,s) are studied, which give the continuation of Eisenstein and Poincaré series. The parameter r is the weight and \(1/4- s^ 2\) is the eigenvalue of the Casimir operator. It is shown that each modular form with at most exponential growth may be obtained as value of a meromorphic combination of analytically continued Poincaré and Eisenstein series.
scientific article; zbMATH DE number 3908516