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We study the number of lattice points in ℝ,
≥ 2, lying inside an annulus as a function of the centre of the
annulus. The average number of lattice points there equals the volume of the annulus, and
we study the
and
norms of
the remainder. We say that a dimension is critical, if these norms do not have upper and
lower bounds of the same order as the radius goes to infinity. In [Duke Math. J., 107 (2001), No. 2,...
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