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 $p$.
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 $p$.
@article{CMUC_1999_40_2_a19,
author = {Kr\"atzel, Ekkehard},
title = {Lattice points in super spheres},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {373--391},
year = {1999},
volume = {40},
number = {2},
mrnumber = {1732659},
zbl = {0993.11050},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_1999_40_2_a19/}
}
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/