Abstract
Very general hypersurfaces in ℝ4 contain ≪r 2+(4/9) integer points in any ball of radiusr>1. As a consequence, an irreducible algebraic hypersurface in ℝn (wheren≥4) which is not a cylinder and is of degreed, contains ≤c(d, n)r n−1−(5/9) integer points in a ball of radiusr. This improves on the known boundc(d, n)r n−(3/2).
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Meinem verehrten Lehrer Professor E. Hlawka zum siebzigsten Geburtstag gewidmet
Written with partial support from NSF-MCS-8211461.
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Schmidt, W.M. Integer points on hypersurfaces. Monatshefte für Mathematik 102, 27–58 (1986). https://doi.org/10.1007/BF01565485
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DOI: https://doi.org/10.1007/BF01565485