## Ekkehard Kr\"atzel

*Lattice points in super spheres *

Comment.Math.Univ.Carolinae 40,2 (1999) 373-391. **Abstract:**In this article we consider the number $R_{k,p}(x)$ of lattice points in $p$-dimensional super spheres with even power $k \ge 4$. We give an asymptotic expansion of the $d$-fold anti-derivative of $R_{k,p}(x)$ for sufficiently large $d$. From this we deduce a new estimation for the error term in the asymptotic representation of $R_{k,p}(x)$ for $p<k<2p-4$.

**Keywords:** lattice points, exponential sums

**AMS Subject Classification:** 11P21

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