Abstract.
An explicit estimate for the lattice point discrepancy of ellipsoids of rotation. For the lattice point discrepancy \(P_{\cal E}(x)\) (i.e., the number of integer points minus the volume) of the ellipsoid (u 1 2 + u 2 2)/a + a 2 u 3 2 ≤ x (a, x > 0), this paper provides an estimate of the form \(\vert P_{\cal E}(x)\vert \le 1237 a^{1/8} x^{11/16} (\log (100x)+\vert \log a\vert )^{3/8} +\) terms of smaller order in x.
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Die Autoren danken dem Österreichischen Fonds zur Förderung der wissenschaftlichen Forschung (FWF) für finanzielle Unterstützung unter der Projekt-Nr. P18079-N12.
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Krätzel, E., Nowak, W. Eine explizite Abschätzung für die Gitter-Diskrepanz von Rotationsellipsoiden. Mh Math 152, 45–61 (2007). https://doi.org/10.1007/s00605-007-0458-4
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DOI: https://doi.org/10.1007/s00605-007-0458-4