The paper gives an identity for a sum of theta-series related to an imaginary quadratic field. This sum is expressed in terms of a certain Eisenstein series. The identity obtained is used in a new proof of the formula for the number of integral points in a system of ellipses. Such formulas are of interest because of their relations to the arithmetic Riemann–Roch theorem.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 479, 2019, pp. 160–170.
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Smirnov, A.L. Eisenstein’s Program and Modular Forms. J Math Sci 249, 104–111 (2020). https://doi.org/10.1007/s10958-020-04924-9
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DOI: https://doi.org/10.1007/s10958-020-04924-9