Distribution of Fourier coefficient values for modular forms of weight 1
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 13, Tome 226 (1996), pp. 196-227
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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.
@article{ZNSL_1996_226_a14,
author = {O. M. Fomenko},
title = {Distribution of {Fourier} coefficient values for modular forms of weight~1},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {196--227},
year = {1996},
volume = {226},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_226_a14/}
}
O. M. Fomenko. Distribution of Fourier coefficient values for modular forms of weight 1. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 13, Tome 226 (1996), pp. 196-227. http://geodesic.mathdoc.fr/item/ZNSL_1996_226_a14/