Distribution of values of Fourier coefficients for modular forms of weight 1

For modular forms of weight, 1, the distribution of values of their Fourier coefficients over polynomial sequences of natural numbers is considered. A new proof of Bernays' theorem is given. It is proved that the error term in the well-known Rankin-Selberg asymptotic formula can be improved for cusp forms associated with binary theta series. Bibliography: 52 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 196–227.