Abstract:
Exact formulas for the number of integral points in certain ellipses are obtained. These formulas generalize a formula of Eisenstein and belong to a rare type of exact formulas for the number of lattice points in curvilinear domains. The obtained formulas can be useful when studying the Riemann–Roch problem for arithmetic varieties.
Key words and phrases:arithmetic curve, Riemann–Roch theorem, Eisenstein, imaginary quadratic field, exact formula, lattice point.
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