Eisenstein’s Program and Modular Forms

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 in...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-10, Vol.249 (1), p.104-111
Main Author: Smirnov, A. L.
Format: Article
Language:English
Subjects:
Fields (mathematics)
Mathematics
Mathematics and Statistics
Number theory
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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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04924-9