On the p-adic Waring's problem

• Autorzy: José Felipe Voloch
• Języki publikacji: EN

Kategorie tematyczne

• 11D88: p -adic and power series fields
• 11P05: Waring's problem and variants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 90
• Numer: 1
• Strony: 91-95

Daty

wydano

1999

otrzymano

1998-10-13

Twórcy

autor

José Felipe Voloch

• Department of Mathematics, University of Texas, Austin, Texas 78712, U.S.A.

Bibliografia

• [Be] N. Benschop, Powersums representing residues mod $p^k$, from Fermat to Waring, preprint, available at http://www.IAE.nl/users/benschop/.
• [B] J. D. Bovey, A note on Waring's problem in p-adic fields, Acta Arith. 29 (1976), 343-351.
• [GV] A. Garcia and J. F. Voloch, Fermat curves over finite fields, J. Number Theory 30 (1988), 345-356.
• [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.