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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2018 Volume 469, Pages 7–31 (Mi znsl6600)

This article is cited in 1 paper

Eisenstein formula and Dirihlet correspondence

D. A. Artyushina, A. L. Smirnovb

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We obtain an exact formula for the number of integral points in the system of ellipses related according to Dirichlet with an arbitrary imaginary quadratic field. The relation of this formula to arithmetic Riemann–Roch theorems is discussed. So far it has been known only nine similar formulas. They correspond to the imaginary quadratic fields with the trivial class group.

Key words and phrases: integral point, Riemann–Roch theorem, exact formula, ellipse, arithmetic.

UDC: 511.2

Received: 01.09.2018


 English version:
Journal of Mathematical Sciences (New York), 2019, 242:4, 470–486

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© Steklov Math. Inst. of RAS, 2024