On Waring's problem in finite fields

Arne Winterhof

Acta Arithmetica (1998)

  • Volume: 87, Issue: 2, page 171-177
  • ISSN: 0065-1036

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Arne Winterhof. "On Waring's problem in finite fields." Acta Arithmetica 87.2 (1998): 171-177. <http://eudml.org/doc/207212>.

@article{ArneWinterhof1998,
author = {Arne Winterhof},
journal = {Acta Arithmetica},
keywords = {Waring problem; finite fields; extension of Chowla-Mann-Straus bound},
language = {eng},
number = {2},
pages = {171-177},
title = {On Waring's problem in finite fields},
url = {http://eudml.org/doc/207212},
volume = {87},
year = {1998},
}

TY - JOUR
AU - Arne Winterhof
TI - On Waring's problem in finite fields
JO - Acta Arithmetica
PY - 1998
VL - 87
IS - 2
SP - 171
EP - 177
LA - eng
KW - Waring problem; finite fields; extension of Chowla-Mann-Straus bound
UR - http://eudml.org/doc/207212
ER -

References

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  1. [1] M. Bhaskaran, Sums of mth powers in algebraic and abelian number fields, Arch. Math. (Basel) 17 (1966), 497-504; Correction, Arch. Math. (Basel) 22 (1971), 370-371. Zbl0281.10025
  2. [2] J. D. Bovey, A new upper bound for Waring's problem mod p, Acta Arith. 32 (1977), 157-162. Zbl0355.10018
  3. [3] S. Chowla, H. B. Mann and E. G. Straus, Some applications of the Cauchy-Davenport theorem, Norske Vid. Selsk. Forh. Trondheim 32 (1959), 74-80. Zbl0109.03206
  4. [4] G. T. Diderrich and H. B. Mann, Representations by k-th powers in GF(q), J. Number Theory 4 (1972), 269-273. Zbl0235.12015
  5. [5] M. M. Dodson, Homogeneous additive congruences, Philos. Trans. Roy. Soc. London Ser. A 261 (1967), 163-210. Zbl0139.27102
  6. [6] M. M. Dodson, On Waring's problem in GF[p], Acta Arith. 19 (1971), 147-173. Zbl0221.10019
  7. [7] M. M. Dodson and A. Tietäväinen, A note on Waring's problem in GF[p], Acta Arith. 30 (1976), 159-167. 
  8. [8] A. Garcia and J. F. Voloch, Fermat curves over finite fields, J. Number Theory 30 (1988), 345-356. Zbl0671.14012
  9. [9] D. R. Heath-Brown and S. Konyagin, New bounds for Gauss sums derived from kth powers and for Heilbronn's exponential sum, submitted to Quart. J. Math. Oxford. Zbl0983.11052
  10. [10] J. R. Joly, Sommes de puissances d-ièmes dans un anneau commutatif, Acta Arith. 17 (1970), 37-114. Zbl0206.34001
  11. [11] S. V. Konyagin, On estimates of Gaussian sums and Waring's problem for a prime modulus, Trudy Mat. Inst. Steklov. 198 (1992), 111-124 (in Russian); English transl.: Proc. Steklov Inst. Math. 1994, no. 1, 105-117. Zbl0820.11048
  12. [12] R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl. 20, Addison-Wesley, 1983. Zbl0554.12010
  13. [13] S. Singh, Analysis of each integer as sum of two cubes in a finite integral domain, Indian J. Pure Appl. Math. 6 (1975), 29-35. Zbl0339.12011
  14. [14] C. Small, Sums of powers in large finite fields, Proc. Amer. Math. Soc. 65 (1977), 35-36. Zbl0328.12016
  15. [15] A. Tietäväinen, On diagonal forms over finite fields, Ann. Univ. Turku Ser. A I 118 (1968), 10 pp. Zbl0157.10401
  16. [16] L. Tornheim, Sums of n-th powers in fields of prime characteristic, Duke Math. J. 4 (1938), 359-362. Zbl0019.00302

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