# On the p-adic Waring's problem

Acta Arithmetica (1999)

- Volume: 90, Issue: 1, page 91-95
- ISSN: 0065-1036

## Access Full Article

top## How to cite

topJosé Felipe Voloch. "On the p-adic Waring's problem." Acta Arithmetica 90.1 (1999): 91-95. <http://eudml.org/doc/207317>.

@article{JoséFelipeVoloch1999,

author = {José Felipe Voloch},

journal = {Acta Arithmetica},

keywords = {Waring's problem; -adic numbers; unramified extension},

language = {eng},

number = {1},

pages = {91-95},

title = {On the p-adic Waring's problem},

url = {http://eudml.org/doc/207317},

volume = {90},

year = {1999},

}

TY - JOUR

AU - José Felipe Voloch

TI - On the p-adic Waring's problem

JO - Acta Arithmetica

PY - 1999

VL - 90

IS - 1

SP - 91

EP - 95

LA - eng

KW - Waring's problem; -adic numbers; unramified extension

UR - http://eudml.org/doc/207317

ER -

## References

top- [Be] N. Benschop, Powersums representing residues mod ${p}^{k}$, from Fermat to Waring, preprint, available at http://www.IAE.nl/users/benschop/. Zbl1013.11002
- [B] J. D. Bovey, A note on Waring's problem in p-adic fields, Acta Arith. 29 (1976), 343-351. Zbl0336.10014
- [GV] A. Garcia and J. F. Voloch, Fermat curves over finite fields, J. Number Theory 30 (1988), 345-356. Zbl0671.14012
- [HB] R. Heath-Brown, An estimate for Heilbronn's exponential sum, in: Analytic Number Theory, Vol. 2 (Allerton Park, Ill., 1995), Progr. Math. 139, Birkhäuser Boston, Boston, Mass., 1996, 451-463.
- [K] N. M. Katz, Number of points on singular complete intersections, appendix to: C. Hooley, On the number of points on a complete intersection over a finite field, J. Number Theory 38 (1991), 338-358.
- [M] D. A. Mit'kin, An estimate for the number of roots of some comparisons by the Stepanov method, Mat. Zametki 51 (1992), 52-58, 157 (in Russian); English transl.: Math. Notes 51 (1992), 565-570.
- [TV] J. Tate and J. F. Voloch, Linear forms in p-adic roots of unity, Internat. Math. Res. Notices 12 (1996), 589-601. Zbl0893.11015

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