Email this article Eisenstein Formula and Dirichlet Correspondence
- Authors: Artyushin D.A.1, Smirnov A.L.2
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Affiliations:
- St. Petersburg State University
- St. Petersburg Department of the Steklov Mathematical Institute
- Issue: Vol 242, No 4 (2019)
- Pages: 470-486
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/242994
- DOI: https://doi.org/10.1007/s10958-019-04491-8
- ID: 242994
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Abstract
In the paper, an exact formula for the number of integral points in the system of ellipses related, according to Dirichlet, to an arbitrary imaginary quadratic field is provided. The relation of this formula to an arithmetic Riemann–Roch theorem is discussed. Previously, only nine formulas of such a type have been known. They correspond to the imaginary quadratic fields with the trivial class group.
About the authors
D. A. Artyushin
St. Petersburg State University
Author for correspondence.
Email: artyushinden@gmail.com
Russian Federation, St. Petersburg
A. L. Smirnov
St. Petersburg Department of the Steklov Mathematical Institute
Email: artyushinden@gmail.com
Russian Federation, St. Petersburg
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