Geodesic
Lattice points in super spheres
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 373-391.

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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 $p$.
Classification : 11P21
Keywords: lattice points; exponential sums 
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     author = {Kr\"atzel, Ekkehard},
     title = {Lattice points in super spheres},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {373--391},
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     number = {2},
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     zbl = {0993.11050},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1999__40_2_a19/}
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Krätzel, Ekkehard. Lattice points in super spheres. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 373-391. http://geodesic.mathdoc.fr/item/CMUC_1999__40_2_a19/