Archiv der Mathematik

, Volume 83, Issue 3, pp 208–216 | Cite as

The lattice point discrepancy of a body of revolution: Improving the lower bound by Soundararajan’s method

Original Paper


For a convex body \(\mathcal{B}\) in \(\mathbb{R}^3 \) which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy\(P_\mathcal{B} (t)\) (number of integer points minus volume) of a linearly dilated copy \(\sqrt t \mathcal{B}\) is estimated from below. On the basis of a recent method of K. Soundararajan [16], an Ω-bound is obtained that improves upon all earlier results of this kind.

Mathematics Subject Classification (2000):

11P21 11K38 52C07 


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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  1. 1.Institut für Mathematik, Department für Integrative BiologieUniversität für Bodenkultur WienWienAustria

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