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 formulas obtained may be useful in studying the Riemann–Roch problem for arithmetic varieties.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 413, 2013, pp. 173–182.
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Smirnov, A. On Exact Formulas for the Number of Integral Points. J Math Sci 202, 448–454 (2014). https://doi.org/10.1007/s10958-014-2054-1
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DOI: https://doi.org/10.1007/s10958-014-2054-1