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

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Abstract

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.

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  1. O. M. Fomenko
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 196–227.

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Fomenko, O.M. Distribution of values of Fourier coefficients for modular forms of weight 1. J Math Sci 89, 1050–1071 (1998). https://doi.org/10.1007/BF02358541

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