Distribution of Fourier coefficient values 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. Bibl. 52 titles.