Steklov Institute of Mathematics at St.Petersburg

PREPRINT 07/2004

VARIATION OF THE NUMBER OF LATTICE POINTS IN LARGE BALLS

This preprint was accepted June 7, 2004

ABSTRACT:
For rational lattices in $\R^d$, $d\ge 4$
we prove lower bounds for the
variation of the number of lattice points
inside balls of large radius with a variable centre.
The obtained estimates are sharp for $d\ge 5$.