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Eisenstein’s program and modular forms. (English. Russian original) Zbl 1451.11032

J. Math. Sci., New York 249, No. 1, 104-111 (2020); translation from Zap. Nauchn. Semin. POMI 479, 160-170 (2019).
Summary: 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.

MSC:

11F27 Theta series; Weil representation; theta correspondences
11F11 Holomorphic modular forms of integral weight
11P21 Lattice points in specified regions
11E41 Class numbers of quadratic and Hermitian forms
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References:

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