Geodesic
On exact formulas for the number of integral points
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 173-182 
A. Smirnov. On exact formulas for the number of integral points. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 173-182. http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a8/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

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[3] G. Eisenstein, “Geometrischer Beweis des Fundamentaltheorems für die quadratischen Reste”, J. für die reine und angew. Math., 28 (1844), 246–248 | DOI | Zbl