# Lattice points in super spheres

Commentationes Mathematicae Universitatis Carolinae (1999)

- Volume: 40, Issue: 2, page 373-391
- ISSN: 0010-2628

## Access Full Article

top## Abstract

top## How to cite

topKrätzel, Ekkehard. "Lattice points in super spheres." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 373-391. <http://eudml.org/doc/248389>.

@article{Krätzel1999,

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 $p<k<2p-4$.},

author = {Krätzel, Ekkehard},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {lattice points; exponential sums; lattice points; exponential sums; super spheres},

language = {eng},

number = {2},

pages = {373-391},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Lattice points in super spheres},

url = {http://eudml.org/doc/248389},

volume = {40},

year = {1999},

}

TY - JOUR

AU - Krätzel, Ekkehard

TI - Lattice points in super spheres

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1999

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 40

IS - 2

SP - 373

EP - 391

AB - 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 $p<k<2p-4$.

LA - eng

KW - lattice points; exponential sums; lattice points; exponential sums; super spheres

UR - http://eudml.org/doc/248389

ER -

## References

top- Copson E.T., Asymptotic Expansions, Cambridge University Press, Cambridge, 1965. Zbl1096.41001MR0168979
- Hoeppner S., Krätzel E., The number of lattice points inside and on the surface $|{t}_{1}{|}^{k}+|{t}_{2}{|}^{k}+...+{\left|{t}_{n}\right|}^{k}=x$, Math. Nachr. 163 (1993), 257-268. (1993) MR1235070
- Krätzel E., Lattice Points, DVW, Berlin, 1988 and Kluwer, Dordrecht-Boston-London, 1988. MR0998378
- Kuba G., On the sums of two k-th powers of numbers in residue classes II, Abh. Math. Sem. Hamburg 63 (1993), 87-95. (1993) MR1227866
- Müller W., Nowak W.G., Lattice points in planar domains: Applications of Huxley's Discrete Hardy-Littlewood-Method, Numbertheoretic analysis, Vienna 1988-1989, Springer Lecture Notes 1452 (eds. E. Hlawka and R.F. Tichy) (1990), pp.139-164.
- Schmidt-Röh R., Ein additives Gitterpunktproblem, Doctoral Thesis, FSU Jena, 1989.
- Schnabel L., Über eine Verallgemeinerung des Kreisproblems, Wiss. Z. FSU Jena, Math.-Naturwiss. R. 31 (1982), 667-681. (1982) Zbl0497.10038MR0682557
- Wild R.E., On the number of lattice points in ${x}^{t}+{y}^{t}={n}^{t/2}$, Pacific J. Math. 8 (1958), 929-940. (1958) MR0112883

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.